diff --git a/tornado/http1connection.py b/tornado/http1connection.py
index 10402b4b..0413fd9a 100644
--- a/tornado/http1connection.py
+++ b/tornado/http1connection.py
@@ -492,7 +492,7 @@ class HTTP1Connection(httputil.HTTPConnection):
         else:
             future = self._write_future = Future()
             self._pending_write = self.stream.write(self._format_chunk(chunk))
-            self._pending_write.add_done_callback(self._on_write_complete)
+            future_add_done_callback(self._pending_write, self._on_write_complete)
         return future
 
     def finish(self) -> None:

RequestHandler.finish() future not resolving
Just tried Tornado 5.1 for the first time and am wondering if I'm doing something wrong when waiting for the future of the `finish` method:

```python
import tornado.ioloop
import tornado.web

class MainHandler(tornado.web.RequestHandler):
    async def get(self):
        print('before')
        await self.finish("Hello, world")
        print('after')

def make_app():
    return tornado.web.Application([
        (r"/", MainHandler),
    ])

if __name__ == "__main__":
    app = make_app()
    app.listen(8888)
    tornado.ioloop.IOLoop.current().start()
```

It seems like the future is never resolved. `after` is not printed and interrupting the application outputs:

```
KeyboardInterrupt
ERROR:asyncio:Task was destroyed but it is pending!
task: <Task pending coro=<MainHandler.get() running at main.py:7> wait_for=<Future pending cb=[<TaskWakeupMethWrapper object at 0x7f0cb0b25e28>()]> cb=[IOLoop.add_future.<locals>.<lambda>() at /home/sebastian/.virtualenvs/tempenv-2fc3210213e1f/lib/python3.6/site-packages/tornado/ioloop.py:719]>
```

Python 3.6, Ubuntu
diff --git a/tornado/test/web_test.py b/tornado/test/web_test.py
index a6f5d1bd..d43d46bc 100644
--- a/tornado/test/web_test.py
+++ b/tornado/test/web_test.py
@@ -224,6 +224,13 @@ class FinalReturnTest(WebTestCase):
                 test.final_return = self.finish()
                 yield test.final_return
 
+            @gen.coroutine
+            def post(self):
+                self.write("hello,")
+                yield self.flush()
+                test.final_return = self.finish("world")
+                yield test.final_return
+
         class RenderHandler(RequestHandler):
             def create_template_loader(self, path):
                 return DictLoader({"foo.html": "hi"})
@@ -243,6 +250,11 @@ class FinalReturnTest(WebTestCase):
         self.assertIsInstance(self.final_return, Future)
         self.assertTrue(self.final_return.done())
 
+        response = self.fetch(self.get_url("/finish"), method="POST", body=b"")
+        self.assertEqual(response.code, 200)
+        self.assertIsInstance(self.final_return, Future)
+        self.assertTrue(self.final_return.done())
+
     def test_render_method_return_future(self):
         response = self.fetch(self.get_url("/render"))
         self.assertEqual(response.code, 200)

pip install -e .
parse_log_pytest
pytest
flake8 mypy black pytest coverage
apt-get update apt-get install -y gcc
3.6
pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
attrs @ file:///opt/conda/conda-bld/attrs_1642510447205/work
black==22.8.0
certifi==2021.5.30
click==8.0.4
coverage==6.2
dataclasses==0.8
flake8==5.0.4
importlib-metadata==4.2.0
iniconfig @ file:///home/linux1/recipes/ci/iniconfig_1610983019677/work
mccabe==0.7.0
more-itertools @ file:///tmp/build/80754af9/more-itertools_1637733554872/work
mypy==0.971
mypy-extensions==1.0.0
packaging @ file:///tmp/build/80754af9/packaging_1637314298585/work
pathspec==0.9.0
platformdirs==2.4.0
pluggy @ file:///tmp/build/80754af9/pluggy_1615976315926/work
py @ file:///opt/conda/conda-bld/py_1644396412707/work
pycodestyle==2.9.1
pyflakes==2.5.0
pyparsing @ file:///tmp/build/80754af9/pyparsing_1635766073266/work
pytest==6.2.4
toml @ file:///tmp/build/80754af9/toml_1616166611790/work
tomli==1.2.3
-e git+https://github.com/tornadoweb/tornado.git@c350dc9f4dfca5ede1002fa578cc33d6b1cea120#egg=tornado
typed-ast==1.5.5
typing_extensions @ file:///opt/conda/conda-bld/typing_extensions_1647553014482/work
zipp @ file:///tmp/build/80754af9/zipp_1633618647012/work

name: tornado
channels:
  - defaults
  - https://repo.anaconda.com/pkgs/main
  - https://repo.anaconda.com/pkgs/r
  - conda-forge
dependencies:
  - _libgcc_mutex=0.1=main
  - _openmp_mutex=5.1=1_gnu
  - attrs=21.4.0=pyhd3eb1b0_0
  - ca-certificates=2025.2.25=h06a4308_0
  - certifi=2021.5.30=py36h06a4308_0
  - importlib_metadata=4.8.1=hd3eb1b0_0
  - iniconfig=1.1.1=pyhd3eb1b0_0
  - ld_impl_linux-64=2.40=h12ee557_0
  - libffi=3.3=he6710b0_2
  - libgcc-ng=11.2.0=h1234567_1
  - libgomp=11.2.0=h1234567_1
  - libstdcxx-ng=11.2.0=h1234567_1
  - more-itertools=8.12.0=pyhd3eb1b0_0
  - ncurses=6.4=h6a678d5_0
  - openssl=1.1.1w=h7f8727e_0
  - packaging=21.3=pyhd3eb1b0_0
  - pip=21.2.2=py36h06a4308_0
  - pluggy=0.13.1=py36h06a4308_0
  - py=1.11.0=pyhd3eb1b0_0
  - pyparsing=3.0.4=pyhd3eb1b0_0
  - pytest=6.2.4=py36h06a4308_2
  - python=3.6.13=h12debd9_1
  - readline=8.2=h5eee18b_0
  - setuptools=58.0.4=py36h06a4308_0
  - sqlite=3.45.3=h5eee18b_0
  - tk=8.6.14=h39e8969_0
  - toml=0.10.2=pyhd3eb1b0_0
  - typing_extensions=4.1.1=pyh06a4308_0
  - wheel=0.37.1=pyhd3eb1b0_0
  - xz=5.6.4=h5eee18b_1
  - zipp=3.6.0=pyhd3eb1b0_0
  - zlib=1.2.13=h5eee18b_1
  - pip:
      - black==22.8.0
      - click==8.0.4
      - coverage==6.2
      - dataclasses==0.8
      - flake8==5.0.4
      - importlib-metadata==4.2.0
      - mccabe==0.7.0
      - mypy==0.971
      - mypy-extensions==1.0.0
      - pathspec==0.9.0
      - platformdirs==2.4.0
      - pycodestyle==2.9.1
      - pyflakes==2.5.0
      - tomli==1.2.3
      - typed-ast==1.5.5
prefix: /opt/conda/envs/tornado

tornado/test/web_test.py::FinalReturnTest::test_finish_method_return_future
tornado/test/web_test.py::SecureCookieV1Test::test_arbitrary_bytes tornado/test/web_test.py::SecureCookieV1Test::test_cookie_tampering_future_timestamp tornado/test/web_test.py::SecureCookieV1Test::test_round_trip tornado/test/web_test.py::SecureCookieV2Test::test_key_version_increment_version tornado/test/web_test.py::SecureCookieV2Test::test_key_version_invalidate_version tornado/test/web_test.py::SecureCookieV2Test::test_key_version_roundtrip tornado/test/web_test.py::SecureCookieV2Test::test_key_version_roundtrip_differing_version tornado/test/web_test.py::SecureCookieV2Test::test_round_trip tornado/test/web_test.py::FinalReturnTest::test_render_method_return_future tornado/test/web_test.py::CookieTest::test_cookie_special_char tornado/test/web_test.py::CookieTest::test_get_cookie tornado/test/web_test.py::CookieTest::test_set_cookie tornado/test/web_test.py::CookieTest::test_set_cookie_domain tornado/test/web_test.py::CookieTest::test_set_cookie_expires_days tornado/test/web_test.py::CookieTest::test_set_cookie_false_flags tornado/test/web_test.py::CookieTest::test_set_cookie_max_age tornado/test/web_test.py::CookieTest::test_set_cookie_overwrite tornado/test/web_test.py::AuthRedirectTest::test_absolute_auth_redirect tornado/test/web_test.py::AuthRedirectTest::test_relative_auth_redirect tornado/test/web_test.py::ConnectionCloseTest::test_connection_close tornado/test/web_test.py::RequestEncodingTest::test_error tornado/test/web_test.py::RequestEncodingTest::test_group_encoding tornado/test/web_test.py::RequestEncodingTest::test_group_question_mark tornado/test/web_test.py::RequestEncodingTest::test_slashes tornado/test/web_test.py::WSGISafeWebTest::test_decode_argument tornado/test/web_test.py::WSGISafeWebTest::test_decode_argument_invalid_unicode tornado/test/web_test.py::WSGISafeWebTest::test_decode_argument_plus tornado/test/web_test.py::WSGISafeWebTest::test_get_argument tornado/test/web_test.py::WSGISafeWebTest::test_get_body_arguments tornado/test/web_test.py::WSGISafeWebTest::test_get_query_arguments tornado/test/web_test.py::WSGISafeWebTest::test_header_injection tornado/test/web_test.py::WSGISafeWebTest::test_multi_header tornado/test/web_test.py::WSGISafeWebTest::test_no_gzip tornado/test/web_test.py::WSGISafeWebTest::test_optional_path tornado/test/web_test.py::WSGISafeWebTest::test_redirect tornado/test/web_test.py::WSGISafeWebTest::test_reverse_url tornado/test/web_test.py::WSGISafeWebTest::test_types tornado/test/web_test.py::WSGISafeWebTest::test_uimodule_resources tornado/test/web_test.py::WSGISafeWebTest::test_uimodule_unescaped tornado/test/web_test.py::WSGISafeWebTest::test_web_redirect tornado/test/web_test.py::WSGISafeWebTest::test_web_redirect_double_slash tornado/test/web_test.py::NonWSGIWebTests::test_empty_flush tornado/test/web_test.py::ErrorResponseTest::test_default tornado/test/web_test.py::ErrorResponseTest::test_failed_write_error tornado/test/web_test.py::ErrorResponseTest::test_write_error tornado/test/web_test.py::StaticFileTest::test_absolute_static_url tornado/test/web_test.py::StaticFileTest::test_absolute_version_exclusion tornado/test/web_test.py::StaticFileTest::test_include_host_override tornado/test/web_test.py::StaticFileTest::test_path_traversal_protection tornado/test/web_test.py::StaticFileTest::test_relative_version_exclusion tornado/test/web_test.py::StaticFileTest::test_root_static_path tornado/test/web_test.py::StaticFileTest::test_static_304_etag_modified_bug tornado/test/web_test.py::StaticFileTest::test_static_304_if_modified_since tornado/test/web_test.py::StaticFileTest::test_static_304_if_none_match tornado/test/web_test.py::StaticFileTest::test_static_404 tornado/test/web_test.py::StaticFileTest::test_static_compressed_files tornado/test/web_test.py::StaticFileTest::test_static_etag tornado/test/web_test.py::StaticFileTest::test_static_files tornado/test/web_test.py::StaticFileTest::test_static_head tornado/test/web_test.py::StaticFileTest::test_static_head_range tornado/test/web_test.py::StaticFileTest::test_static_if_modified_since_pre_epoch tornado/test/web_test.py::StaticFileTest::test_static_if_modified_since_time_zone tornado/test/web_test.py::StaticFileTest::test_static_invalid_range tornado/test/web_test.py::StaticFileTest::test_static_range_if_none_match tornado/test/web_test.py::StaticFileTest::test_static_unsatisfiable_range_end_less_than_start tornado/test/web_test.py::StaticFileTest::test_static_unsatisfiable_range_invalid_start tornado/test/web_test.py::StaticFileTest::test_static_unsatisfiable_range_zero_suffix tornado/test/web_test.py::StaticFileTest::test_static_url tornado/test/web_test.py::StaticFileTest::test_static_with_range tornado/test/web_test.py::StaticFileTest::test_static_with_range_end_edge tornado/test/web_test.py::StaticFileTest::test_static_with_range_full_file tornado/test/web_test.py::StaticFileTest::test_static_with_range_full_past_end tornado/test/web_test.py::StaticFileTest::test_static_with_range_neg_end tornado/test/web_test.py::StaticFileTest::test_static_with_range_neg_past_start tornado/test/web_test.py::StaticFileTest::test_static_with_range_partial_past_end tornado/test/web_test.py::StaticDefaultFilenameTest::test_static_default_filename tornado/test/web_test.py::StaticDefaultFilenameTest::test_static_default_redirect tornado/test/web_test.py::StaticFileWithPathTest::test_serve tornado/test/web_test.py::CustomStaticFileTest::test_serve tornado/test/web_test.py::CustomStaticFileTest::test_static_url tornado/test/web_test.py::HostMatchingTest::test_host_matching tornado/test/web_test.py::DefaultHostMatchingTest::test_default_host_matching tornado/test/web_test.py::NamedURLSpecGroupsTest::test_named_urlspec_groups tornado/test/web_test.py::ClearHeaderTest::test_clear_header tornado/test/web_test.py::Header204Test::test_204_headers tornado/test/web_test.py::Header304Test::test_304_headers tornado/test/web_test.py::StatusReasonTest::test_status tornado/test/web_test.py::DateHeaderTest::test_date_header tornado/test/web_test.py::RaiseWithReasonTest::test_httperror_str tornado/test/web_test.py::RaiseWithReasonTest::test_httperror_str_from_httputil tornado/test/web_test.py::RaiseWithReasonTest::test_raise_with_reason tornado/test/web_test.py::ErrorHandlerXSRFTest::test_404_xsrf tornado/test/web_test.py::ErrorHandlerXSRFTest::test_error_xsrf tornado/test/web_test.py::GzipTestCase::test_gzip tornado/test/web_test.py::GzipTestCase::test_gzip_not_requested tornado/test/web_test.py::GzipTestCase::test_gzip_static tornado/test/web_test.py::GzipTestCase::test_vary_already_present tornado/test/web_test.py::GzipTestCase::test_vary_already_present_multiple tornado/test/web_test.py::PathArgsInPrepareTest::test_kw tornado/test/web_test.py::PathArgsInPrepareTest::test_pos tornado/test/web_test.py::ClearAllCookiesTest::test_clear_all_cookies tornado/test/web_test.py::ExceptionHandlerTest::test_http_error tornado/test/web_test.py::ExceptionHandlerTest::test_known_error tornado/test/web_test.py::ExceptionHandlerTest::test_unknown_error tornado/test/web_test.py::BuggyLoggingTest::test_buggy_log_exception tornado/test/web_test.py::UIMethodUIModuleTest::test_ui_method tornado/test/web_test.py::GetArgumentErrorTest::test_catch_error tornado/test/web_test.py::SetLazyPropertiesTest::test_set_properties tornado/test/web_test.py::GetCurrentUserTest::test_get_current_user_from_ui_module_is_lazy tornado/test/web_test.py::GetCurrentUserTest::test_get_current_user_from_ui_module_works tornado/test/web_test.py::GetCurrentUserTest::test_get_current_user_works tornado/test/web_test.py::UnimplementedHTTPMethodsTest::test_unimplemented_standard_methods tornado/test/web_test.py::UnimplementedNonStandardMethodsTest::test_unimplemented_other tornado/test/web_test.py::UnimplementedNonStandardMethodsTest::test_unimplemented_patch tornado/test/web_test.py::AllHTTPMethodsTest::test_standard_methods tornado/test/web_test.py::PatchMethodTest::test_other tornado/test/web_test.py::PatchMethodTest::test_patch tornado/test/web_test.py::FinishInPrepareTest::test_finish_in_prepare tornado/test/web_test.py::Default404Test::test_404 tornado/test/web_test.py::Custom404Test::test_404 tornado/test/web_test.py::DefaultHandlerArgumentsTest::test_403 tornado/test/web_test.py::HandlerByNameTest::test_handler_by_name tornado/test/web_test.py::StreamingRequestBodyTest::test_close_during_upload tornado/test/web_test.py::StreamingRequestBodyTest::test_early_return tornado/test/web_test.py::StreamingRequestBodyTest::test_early_return_with_data tornado/test/web_test.py::StreamingRequestBodyTest::test_streaming_body tornado/test/web_test.py::DecoratedStreamingRequestFlowControlTest::test_flow_control_chunked_body tornado/test/web_test.py::DecoratedStreamingRequestFlowControlTest::test_flow_control_compressed_body tornado/test/web_test.py::DecoratedStreamingRequestFlowControlTest::test_flow_control_fixed_body tornado/test/web_test.py::NativeStreamingRequestFlowControlTest::test_flow_control_chunked_body tornado/test/web_test.py::NativeStreamingRequestFlowControlTest::test_flow_control_compressed_body tornado/test/web_test.py::NativeStreamingRequestFlowControlTest::test_flow_control_fixed_body tornado/test/web_test.py::IncorrectContentLengthTest::test_content_length_too_high tornado/test/web_test.py::IncorrectContentLengthTest::test_content_length_too_low tornado/test/web_test.py::ClientCloseTest::test_client_close tornado/test/web_test.py::SignedValueTest::test_expired tornado/test/web_test.py::SignedValueTest::test_key_version_retrieval tornado/test/web_test.py::SignedValueTest::test_key_versioning_invalid_key tornado/test/web_test.py::SignedValueTest::test_key_versioning_read_write_default_key tornado/test/web_test.py::SignedValueTest::test_key_versioning_read_write_non_default_key tornado/test/web_test.py::SignedValueTest::test_known_values tornado/test/web_test.py::SignedValueTest::test_name_swap tornado/test/web_test.py::SignedValueTest::test_non_ascii tornado/test/web_test.py::SignedValueTest::test_payload_tampering tornado/test/web_test.py::SignedValueTest::test_signature_tampering tornado/test/web_test.py::XSRFTest::test_cross_user tornado/test/web_test.py::XSRFTest::test_distinct_tokens tornado/test/web_test.py::XSRFTest::test_refresh_token tornado/test/web_test.py::XSRFTest::test_versioning tornado/test/web_test.py::XSRFTest::test_xsrf_fail_argument_invalid_format tornado/test/web_test.py::XSRFTest::test_xsrf_fail_body_no_cookie tornado/test/web_test.py::XSRFTest::test_xsrf_fail_cookie_invalid_format tornado/test/web_test.py::XSRFTest::test_xsrf_fail_cookie_no_body tornado/test/web_test.py::XSRFTest::test_xsrf_fail_no_token tornado/test/web_test.py::XSRFTest::test_xsrf_success_header tornado/test/web_test.py::XSRFTest::test_xsrf_success_non_hex_token tornado/test/web_test.py::XSRFTest::test_xsrf_success_post_body tornado/test/web_test.py::XSRFTest::test_xsrf_success_query_string tornado/test/web_test.py::XSRFTest::test_xsrf_success_short_token tornado/test/web_test.py::XSRFCookieKwargsTest::test_xsrf_httponly tornado/test/web_test.py::FinishExceptionTest::test_finish_exception tornado/test/web_test.py::DecoratorTest::test_addslash tornado/test/web_test.py::DecoratorTest::test_removeslash tornado/test/web_test.py::CacheTest::test_multiple_strong_etag_match tornado/test/web_test.py::CacheTest::test_multiple_strong_etag_not_match tornado/test/web_test.py::CacheTest::test_multiple_weak_etag_match tornado/test/web_test.py::CacheTest::test_multiple_weak_etag_not_match tornado/test/web_test.py::CacheTest::test_strong_etag_match tornado/test/web_test.py::CacheTest::test_strong_etag_not_match tornado/test/web_test.py::CacheTest::test_weak_etag_match tornado/test/web_test.py::CacheTest::test_weak_etag_not_match tornado/test/web_test.py::CacheTest::test_wildcard_etag tornado/test/web_test.py::RequestSummaryTest::test_missing_remote_ip tornado/test/web_test.py::HTTPErrorTest::test_copy tornado/test/web_test.py::ApplicationTest::test_listen tornado/test/web_test.py::URLSpecReverseTest::test_non_reversible tornado/test/web_test.py::URLSpecReverseTest::test_reverse tornado/test/web_test.py::URLSpecReverseTest::test_reverse_arguments tornado/test/web_test.py::RedirectHandlerTest::test_basic_redirect tornado/test/web_test.py::RedirectHandlerTest::test_redirect_pattern tornado/test/web_test.py::RedirectHandlerTest::test_redirect_with_appending_argument tornado/test/web_test.py::RedirectHandlerTest::test_redirect_with_argument
tornado/http1connection.py
tornado/http1connection.py