As a followup, I do realize that the op-amp does not have a resistor on it's positive leg to counteract the input bias current as it should for a precision integrator. Obviously you'd want to use something like a JFET input op-amp with low input bias current and a resistor that on the positive leg that is equal to the equivalent resistance seen from the negative leg to mitigate integrator error.
Like I said previously, however, this is just a quick schematic for a proof of concept and the values don't really matter nor does it have all the trappings of something you'd want to build.