Integration testing looks for plausible faults in function calls. That's not necessarily the case. As written, the code searches for the first slash when it should search for the last. What I call integration test design searches for the first and third types. The search depends on an examination of the behaviors of the called function.
Integration testing applies to variables as well as to functions.
You test whether the using code handles each kind of value. Integration testing is about finding faults in the calling code, not the called code. The function call is used as a clue, a way to find test requirements that exercise the calling code. It may be a method belonging to one of many classes. When the code accesses it, it may get an unexpected value.