Op-amps intrinsically behave like low-pass filters, due to their stray capacitance
(so they look a bit like the 
circuit). There will pretty much always be some
roll-off at high-enough frequency. For op-amp integrators and differentiators,
this intrinsic frequency response gets combined with the frequency response due to
the impedance of the capacitors at the input or in the feedback loop.
So for example, if you put in a capacitor at the input to make an active
high-pass filter (differentiator), in combination with the intrinsic high-frequency
roll-off, you'll end up with an active band-pass filter.