This can be modified to an ideal integrator circuit, if we replace the feedback resistor Rf by a capacitor C as shown below.
In an ideal op amp the voltage at non inverting input terminal is same as that of inverting input.
Here, in the circuit, as the non inverting input is grounded, the electric potential of inverting input will also be zero as non inverting input. In an ideal op amp, no current entires to the op amp through both inverting and non inverting inputs.
Now, if we apply Kirchhoff current law at node 1 of the above circuit, shown in figure 2, we get,
Integrating both side, we get, This is the integral function of input voltage.