i do integration tests with PHPUnit as well, its just a framework with assert methods. i dont really need to use phpspec or behat or selenium, the kind of tests differ on the context you test, not the tools. as i told, the reason why i use phpunit is that phpunit generates a code coverage, which actually shows you that the code executed a part of a file during the test, this way you know exactly where you can start to refactor and which methods you can ignore. (well this is the theory 
the reallity is a bid harder )