Integration testing means we will combine the individual 
modules of the system.One module is integrated with another 
module.The output of the first moudle it should be input of 
the another module.
syatem testing is nothing but end to end testing. While 
during system testing we will cover all the modules of the 
system

Integration testing :
                      This comes under levels of testing, 
this is basically whitebox testing and main purpose of 
doing integration testing to check the communication 
interface between the unit tested module or submodules.Here 
Dummy modules like stubs and drivers are used to do 
integration testing.
Example:

A--->B--->C-->D

Here we are checking the interface from A to D


System testing:
               The testing done on a whole to check the 
functiolity and requirements are as per the clients 
requirements etc.It is commonly called as black box testing

                   A
                   |
             ________________
             |               |
             |               | 
             B               C
             |               | 
             |               | 
             D_______________E