Say you want to evaluate $\displaystyle \int^{2}_{0} \int^{1}_{0} |x-y| \ dx \ dy $
That's equivalent to evaluating $\displaystyle \int^{1}_{0} \int^{1}_{y} (x-y) \ dx \ dy \ + \int^{1}_{0} \int ^{2}_{x} (y-x) \ dy \ dx $ , right?
Say you want to evaluate $\displaystyle \int^{2}_{0} \int^{1}_{0} |x-y| \ dx \ dy $
That's equivalent to evaluating $\displaystyle \int^{1}_{0} \int^{1}_{y} (x-y) \ dx \ dy \ + \int^{1}_{0} \int ^{2}_{x} (y-x) \ dy \ dx $ , right?