Why might you want to zero out the output voltage before applying an AC signal to the circuit?

Specifically for this circuit: http://i812.photobucket.com/albums/zz41/uofmx12/E21ckt-1.jpg

 

Probably to provide short term compensation of the (non-ideal) amplifier input offset voltage, which in the uncompensated state would lead to a drift in the mean value of the integrator output. At worst case this might lead to the output drifting up or down to saturate near either supply rail. The compensation may require periodic re-adjustment since the input offset itself tends to drift with things like ambient temperature variations and the passage of time.