If the circuit is used as a boxcar (switched reset) integrator then the circuit will work as shown as long as the integrate time is not too long. During the integrate time the input bias current is supplied by the capacitors and will cause a small offset, depending upon the bias current, cap sizes and integrate time. When the cap is reset to 0V the bias charge is dumped and the bias current will travel through the switch as long as it is closed.
If you need to supply DC from the input source, then just add a resistor in parallel with Cin.