What is the purpose of a resistor on the non-inverting terminal of an Op-Amp Integrator?
It depends on the opamp.  In the old days when we had to trudge to school barefoot in the snow uphill both ways, opamps inputs drew enough current to matter to many circuits.  For such opamps, the imbalance in current between the two inputs, called the input offset current was lower than the total current drawn by each input.  You could cancel out the common current drawn by both inputs by driving them with the same impedance, leaving the additional voltage offset due to the lower offset current.  In your example, R3 is there to present the same impedance to the + input as is driving the - input, which is R1//R2.

Generally, this is the case with opamps that have bipolar transistors on the input, such as the common jellybean LM324.

Today a lot of ompamps have MOS inputs, so the input bias current is so low as to not matter in most cases.  Since the current is due to leakage and not biasing the internal transistors, you can't really count on its direction.  There generally is no bias current offset spec.  In this case, there is no point in trying to match the impedance driving each input.  You do sometimes see this on MOS-input opamps due to a religious conviction or someone applying a rule of thumb without thinking about what it's for and when it's valid.