I'd probably refer to any tests that are actually going end-to-end through client request, routing, controller, model, storage, view "End to End tests" or "acceptance tests".
In some integration tests it'd fine, depending what integration (how your code integrates with someone else's code) yer testing.
If you were testing how yer code interacts with the framework: you'll need to load the framework, obvs.
Although for like adapter-level integration tests I'd just want to instantiate the adapter by hand, and not involve anything unnecessary.
Rule of thumb, a test should use only whichever support services are needed for the SUT to operate for the given style of test.
Another rule of thumb: each external support service one needs to exercise the test should raise another flag. Raised flags might be fine. But they should be assessed.
I would say if yer unit tests need to have the framework running, either yer app or the framework is poorly designed.