The region is bounded by the line y=-x and the parabola x=y^2, and thus is in the fourth quadrant. For the order of integration in question, you have the outer integral's limits right. For the inside, recall that your limits will be your y as a function of x, and examining the order, you see that at a given x, y ranges from to -x. Graphing the region in question will help make this more clear.

--Kevin C.