Is there a Maintenance Plan that checks my database for corruption?
Good question. The integrity check in the maintenance plan is enough since it will run a dbcc checkdb.
From MSDN:
integrity check

The Check Database Integrity task encapsulates the DBCC CHECKDB statement.

Running this task will be resource intensive. You don't want to do this in prod. servers if you don't have a maintenance window.
The common way is the following:
1. Backup your databases
2. Restore your db's on a test environment
3. Run a dbcc checkdb on your databases.
This way you check your DB integrity and verify your backup.