Inject SQL_CALC_FOUND_ROWS into db_select()? I've recently learned that SQL_CALC_FOUND_ROWS can give the number of rows in a table from almost any SELECT statement. It's raw SQL syntax is SELECT SQL_CALC_FOUND_ROWS field1, field2, ... FROM ...

Is there an existing way I can that inject that syntax into db_select()?

I want to use this for creating a pager, so I'm already selecting some rows in the first place. It would be handy to get a count out of the query I'm already running. Doing a separate count query would be extra work in my case.
As made evident in Compare db_query() and db_select() performance, db_query() is faster than db_select(), which should then be used when you need to make the query you are executing alterable from other module via hook_query_alter(), for example when you need to get a list of nodes for which a user has access.

If that is not your case, then you can use db_query() and using the query you are showing is quite straight as db_query("SELECT SQL_CALC_FOUND_ROWS field1, field2 FROM ...").