So with double integrals the difficulties can be with setting up the limits to describe the region of integration, R, and choosing the order in which you integrate. Now for this problem you are given the limits which is very nice. It is also good because you are integrating over a rectangle with fixed endpoints. Sometimes you have to integrate over regions defined by other functions, like y=x, and this becomes more tricky.
Since you have your region and limits already given to you, now you must decide in what order to integrate. Which order is best? dxdy or dydx?