This is what unit testing was originally described as. Which confirms my belief that unit testing and integration testing has always been the very same thing.

> Individual methods, especially ones that don't interact with data outside what is passed into them (functional methods), are good for unit testing.

Perhaps unit testing has come to mean this, but these kinds of tests are rarely ever worth writing, so it is questionable if it even needs a name. Sometimes it can be helpful to isolate a function like that for the sake of pinning down complex logic or edge cases, but is likely you'll want to delete this kind of test once you're done. This is where testing brittleness is born.