integration comes under whitebox testing.after complication of 
coding and coresponding unit testing devlopers conduct
integration testing to ensure inter connection between modules.
testing on externsl interface is called black box testing or
system testing.here we are validating application beheaver
in terms of completeness and correctness.system testing is
the single phase of testing where we conduct usibility
testing,functional testing and usibility testing.system
testing is done to ensure that the application is ready to
move towards customer acceptance testing.

As the name indicates, integration testing is used to test 
the integrity of multiple components(modules) in a system.
system testing is the testing at large, which tests the 
complete behavior of the system among multiple modules with 
respect to interface/system platforms.