Fall time for integrator with a large resistor
The circuit you have drawn is NOT an integrator - it is a unity gain inverting amplifier with a low-pass 3dB cut-off of 0.053 Hz.

If you put +2V on the input, the output would become -2V i.e. it wouldn't go to zero. It would reach 99% of -2V in approximately 5*C*R seconds = 15 seconds.

Here's a picture of the frequency response for the low pass and the high pass filter: -



Picture stolen from here