@Rouben Rostamian  

It would seem that this argument is only relevant for y=\pm1. More generally the result that maple is giving makes no sense (to me) for |y|>1 since the argument of the delta is strictly positive.

Taking a step back, if I were actually interested in the following

int(int( Dirac(x^2+y^2-1), x = -infinity..infinity ),y=-infinity..infinity)

The result should be pi (as can be verified by making a change of variables to polar coordinates), but maple resports infinity.