The schematic shows a COHERENT FSK demodulator, not incoherent. In principle it is a synchronous detector or analog multiplier which, by using the analog switch, multiplies the"FSK" input signal with the rectangular reference signal (carrier) which must be obtained elsewhere (not shown). If both signals are in-phase, after each sampling switch the integrator capacitor charges up to a maximum voltage. If they are out-of-phase, the capacitor remains low .
The low-pass filters reject the RF spectrum allowing only modulation spectrum at the output(s).
The unity-gain opamps before the filters isolate the integrators from the LP filters.
The important part is not shown: the FSK carrier retrieval circuit.
The mathematical theory is simple : the switch is a multiplier and the RC circuits after it is the integrator.
Try a book on FSK demodulation or on synchronous detection. Or build and test the circuit.