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U1 is configured as an inverting amplifier - with a twist. As in the regular inverting amp, U1 aims to keep V- = V+ = 0 V. So, applying Vin causes current Iin = Vin/Ri. In the case of a feedback resistor, the opamp output responds by dropping negative and drawing Iin away, maintaining the balance. But here, the current through Cf is proportional to dVout/dt: the slope. So, applying a constant positive input voltage causes Iin. The opamp output starts to swing low, which draws current thruogh Cf, achieving equilibrium. But the output must continue dropping to keep current flowing through Cf. The result is that Vout integrates Vin. This circuit is used in ramp and triangle wave generators. The switch is to manually cancel any initial DC offset. In a practical application, there would need to be a means of dealing with DC offset.
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