All the modules have to be Unit Tested first.
It is better to do step-by-step integration than 
integrating all the modules at once. i.e., if there are 10 
modules, we start by integrating 2 modules first. In this 
integration testing, we have to check

1)whether the dataflow is smooth across the interface of 
the 2 modules. 
2)whether the 2 modules together achieve the intended 
purpose
3)whether a module has a bad effect on another module, by 
giving different sets of data that traverses both the 
modules.

we test functional flow and data flow between the added 
modules.
 this is done with the help of work flows prepared by the 
testers those who has the strong functional knowledge on 
the application in the team.