Why does the feedback resistor change?
There is an outer loop provided by Rf and an inner loop provided by the local integrator capacitor Cf. At low frequencies Cf has effectively a high impedance and the outer loop dominates. This can be approximated by an open Cf and zero value Rf (since Rf impedance would be much lower than OpAmp input impedance).

While at high frequencies CF has lower impedance than Rf path and the inner loop dominates. This can be approximated as shorted Cf and open Rf.