Output Drift of an operational Integrator
Even for Vin=0 the output voltage will ramp up to the maximum (supply rails) due to the finite output offset voltage (input offset times open-loop gain). This cannot be avoided for stand-alone integrators. In many cases, a resistor in parallel to the feedback capacitor can limit this unwanted DC output. The corresponding DC output voltage is Vin*Acl (closed-loop DC gain). However, at the same time, the integrating function is somewhat disturbed (for low frequencies) because the integrator has become a first order lowpass. hence, a trade-off is necessary regarding the resistor value (as large as possible and as low as necessary).

But note, that this problem does NOT exist in case the integrator is used as part of an overall negative feedback loop (as is the case for many control loop sysytems)..