I know this resistor is to prevent the circuit from saturating (caused by offset voltage and input bias current). Who can tell me more details about this resistor?
tau = 100Mohm x 1.59nF = 159 mSec is self-reset tau time constant. For signals much shorter than tau, the circuit acts as integrator. When signal is gone back to 0 the output will decay as exp(-t/tau). E.g. https://www.analog.com/media/en/training-seminars/design-handbooks/ray-stata-op-amp-articles/Operational-Integrators.pdf
The previous answer is OK, but it is also important that the DC voltage at the non-inverting input is amplified 1+100M/100k times, i.e. 1001 times.
As you said, R2 is neccessary to give a path to the DC current from the output, otherwise the circuit will saturate, as can be seen in the schematic diagram without R2 in the figure in the answer of Clyde Eisenbeis . This component, together with the capacitor, also defines the minimum frequency that the circuit behaves as an integrator. This frequency is given by the formula f=1/(2*pi*R2*C1). Below this frequency, the gain is constant and is given by the formula Av=-R2/R1.
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