It's not quite simple as that. The multivariate function that I'm integrating requires two iterated integrals, and the bounds for the inner integrand, I'm pretty sure, need to expressed as a function of one of the two variables.
If you have a double integral like this
The limits c and d on the y integral are c=x and d=-x^{2}
The limits a and b on the x integral are a=0 and b=-1 as minoanman shows in his graph
You may wonder why I said c=x and d=-x^{2} not d=x and c=-x^{2}. x is always higher than -x^{2} and you want to integrate in the positive direction of y so the integral limits are FROM the lower value TO the higher value.
I didn't mean to waste anyone's time. I just thought I'd keep things simple by giving the part of the problem that was putting me off--that and the fact it takes me a long time to do anything in LaTex. But I'll keep that in mind next time.