How can I run integration tests after building all modules in a multi-module Maven project?

I am working on a large multi-module Maven project. Each module has fast unit tests (using the Surefire plugin), many modules have slow integration tests (using the Failsafe plugin).

I would like to speed up the feedback for "simple" build failures (compilation errors and unit test failures) by running integration tests from all modules after all modules have been built and unit-tested.

Can you suggest a good way of achieving this?