Due to a considerable lack of rails integration testing tutorials/guides, here are my notes.
Much better to have a separate environment for integration tests. Follow the Rails guide to create one. Be careful to edit the session domain in the integration.rb file if necessary:
config.session_store :cookie_store, key: '_workable_session', domain: 'test.host'
If the domain is different from what your app expects, you will be losing your session across your requests.