Ideal integrator op-amp DC offset at output?
The initial condition at the start of the simulation is computed by the simulator by inserting conductances (with value gmin) to ground. It is thanks to this it "knows" that the output of the amplifier will start at 0 Volt at t=0. 

To change the initial condition you can either insert a load resistor to the desired voltage, or you can (in most simulators) override the initial condition with an .IC statement.  

If you are happy with 0 Volts as the initial condition and the average (DC) value, then you need to change the phase of the square wave so the first edge comes after 1/4 of the period.