Auto Zero Circuit on AD625 datasheet
The circuit indeed is an integrator. It integrates the non-zero output of the opamp and immediately also offsets it, until the opamp outputs zero, at which point the integrator's output won't change anymore.

If you have any function \$y_i(t)\$, which represents the signal you want to integrate, the function you integrate with the opamp will look like this:
$$
y_s(t) =
\left\{
 \begin{array}{ll}
  y_i(t) &amp;\mbox{if } t_1 &lt; t &lt; t_2\\
  0 &amp; otherwise
 \end{array}
\right.
$$

Where \$t_2 - t_1\$ is the time the switch of the AD7510DIKD is closed.

If you integrate over \$y_s(t)\$ now, you'll get the following:

\$\int_{-\infty}^{\infty}y_s(t)\mathrm{d}t = \int_{-\infty}^{t_1}0\mathrm{d}t + \int_{t_1}^{t_2}y_s(t)\mathrm{d}t + \int_{t_2}^{\infty}0\mathrm{d}t = \int_{t_1}^{t_2}y_s(t)\mathrm{d}t\$

As you can see the output signal will remain constant once the input is zero.