Your answer for the iterated integral should be ∫ 30 ∫ −3−yx2dxdy + ∫ 0−3 ∫ −3yx2dxdy + ∫ 03 ∫ y3x2dxdy + ∫ −30 ∫ −y3x2dxdy. This is a very interesting example which shows that iterated integrals have a life of their own, not just as a method for evaluating double integrals.