The parallel resistor Rp provides a fixed dc gain that is needed for a stable operating point.
However, it disturbs the integrating function because it changes the circuit into a 1st order lowpass.
Thus, integration (with a phase shift of 90 deg) is possible only for frequencies far above (factor 10, at least) the respective corner frequency (1/RpC). In fact, an exact phase shift of 90 deg. occurs at one single frequency only.
There is a higher limit of the usable frequency range due to the frequency dependent gain properties of the opamp .
I hope this answers your question.