Example - Examples help explain so much more than definitions so let me create an example to step through.
Imagine a Web application that requires a login. To keep the example simple, let's imagine a login page that requires an account name and password. A unit test might be built to check the field length of both fields and maybe that the login button doesn't become enabled until a value of the required length is entered in both fields. An integration test, in this example, might be checking that the user views a home page after entering valid values and pressing the login button. So now let's consider the original question and think through what additional tests a functional tester might execute given the unit and integration tests that have been outlined.