Pulse-excited integrator reaching infinite potential?
You haven't done anything wrong. The first stage of your circuit is an integrator, and when you integrate a step function (your input) you get a ramp. Since your input never ends, the ramp never ends and the final value is infinity.

Of course, this only holds for an ideal op-amp. In a real op-amp, output voltages would be limited to the rail voltage.

In case you're wondering, I've never seen the output voltage limitations accounted for in equations. You just have to introduce a nonlinear element into the model (a voltage limiter) and then all of your linear equations are essentially out the window.  In other words, the linear equations you're used to are all well and good as long as the output of any of your stages doesn't exceed the rail voltage - as it will in this case.