Software Development without Integration Testing

Scenario:

I developed a piece of software code. The software module is in isolation, meaning it's not connected to any type of web-service, or external components which it should eventually connect to, to work. I, then, unit tested it by stubbing out (or mocking) the real objects.

Questions:

• From an SDLC point of view, is my development task considered done, without an integration testing?

• Is it safe to hand over the developed module to the testing team (consisting of only manual testers)?

Please, if possible, also mention any reliable sources to backup your explanation