In the circuit in Fig. 1, ICla produces the integral term required but also has the side effect of producing a proportional term not required, so this term is subtracted by IClb leaving a pure integral. If the ratio R2/R5 does not exactly match the ratio of R3/R4, the subtraction will not be complete and a small amount of the proportional term will reach the output. The result of this with a square wave input is shown in Fig. 3a as small steps in the output waveform at points X and Y. This effect can be completely removed by using the simplified circuit shown in Fig. 2. Here the signal is pre-inverted by ICla, then fed to a standard inverting integrator IClb.
The result is a non-inverting integrator with the advantage that the unwanted proportional term is never produced, so it does not need to be subtracted.