White box testing refers to testing that works with the application's internals (or code). White box (or glass box) testing is typically done by developers using the IDE, debugger, and unit tests. This is going into the deep of logic & verifies the function.
Integration testing is considered functional, or black box, testing. Testers write test cases that indicate a given input into the application. Based on this input, they make assumptions about the output of the application. The testers then execute these integration tests as a black box. That is, they do not care about what happens inside the box (the code); they simply care that they get the expected results based on the given input.
Source:- 70-547 training kit book