Integration testing : Integration testing is testing of 
combined parts of an application to determine if they 
function together correctly. The parts can be code modules, 
individual applications, client and server applications on 
a network, etc. This type of testing is especially relevant 
to client/server and distributed systems.
 
System testing: To check the Functionality of the 
application.
System testing is black-box type testing that is based on 
overall requirements specifications. It covers all combined 
parts of a system.

Integration testing:After finishing coding developers will 
do.
System tesing: System testing is done by testers.
System testing consists of following types namely Sanity 
testing,Smoke testing,Performence testing,User acceptence 
testing,functionals testing.

when individual modules of code are integrated into a 
single component,testing done at that time is called 
integration testing .Developer and tester do it.
Two types of integration testing - Top down,Bottom up
integration
System testing - testing entire system as a whole in test 
environment is called system testing

Integration Testing... 
           two units that have already been tested are 
combined into a component and the interface between them is 
tested.
System Testing...
          In System Testing  After complition of 
Integration Testing we test the whole application with test 
data