Choosing the shunt resistor value and capacitor for op-amp integrator based on input resistance and DC gain
The DC gain requirement (ignore the capacitor) requires the shunt resistor to be 1M for a DC gain of -100.
The capacitor is found from half the waveform (100us) times a rule of thumb multiplier of 5 to 10, and we will use 10, for a time constant of 1ms= R1*C.