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Code is integrated and tested after a few hours—a day of development at most. One simple way to do this is to have a machine dedicated to integration. When the machine is free, a pair with code to integrate sits down, loads the current release, loads their changes (checking for and resolving any collisions), and runs the tests until they pass (100% correct).
Integrating one set of changes at a time works well because it is obvious who should fix a test that fails—we should, since we must have broken it, since the last pair left the tests at 100%. And if we can't get the tests to run at 100%, we should throw away what we did and start over, since we obviously didn't know enough to be programming that feature (although we likely do know enough now).