Objective: 

To show the lowpass filtering effect of integrating a signal. 
Steps: 

Consider the square wave shown in the diagram. By adding the
area 'under the curve' we can graphically observe the effect of
integrating the signal. However, we need to resort to mathematics
to determine the frequency content of the signal. 



We have seen the mathematical representation of a square wave
before (see here). If we integrate
this series on a term by term basis we get the expression for
a triangular wave.
From the differences in frequency response we discover the lowpass
filtering effect of the integration process. 