Integration is obtained by reversing the resistor and the capacitor as shown in figure below.
The capacitor is now in the feedback loop.
Opamp integration Circuit
Analysis gives
or
Using dV/dt=I/C gives
and thus the same result as above.
The frequency response is shown in figure below
We can combine the above inverting, summing, offset, differentiation and integration circuits to build an analog computer that can solve differential equations. However, today, the differentiators and integrators are mainly used to condition signals.