Since you've already compiled and tested each individual method, the only thing left is integration testing -- making sure the methods work correctly together.
How could they not? Usually because you've failed to follow contracts somewhere. Perhaps one method takes in two String parameters in a particular order, and another method calls the first method with the arguments in the wrong order. Perhaps one method returns a Snark object, but another method expects it to return a Boojum object.
Errors found in integration testing are usually harder to find and fix than errors found in unit testing, because they can't be pinned down to one small chunk of Java code but are instead problems with the whole program. So anything you can do to find errors earlier will pay off in saved time.
We'll discuss this more as the semester goes on.