The image from BH1750FVI datasheet. http://rohmfs.rohm.com/en/products/databook/datasheet/ic/sensor/light/bh1750fvi-e.pdf (page 4) I don't know why it has the capacitor connect output and input of OpAmp? Can anyone help me about this?
The block diagram is only an approximation of the whole circuit. But essentially a capacitor in the feedback turns the amplifier into an integrator.
The photodiode sensor on the front end of the diagram probably only outputs micro amps. Using an integrator probably allows them to achieve more accurate measurements because it reduces the bandwidth, and thus the noise power. Integrating a weak noisy signal for a long time can give you a clean precise signal.