Sure it is possible! Usually (although not always) when integrating a function f(x), it is possible to find a primitive function F(x). Then the integral of f from

to

will be the difference

.

Say that you instead have a function

that you want to integrate two times, one time with respect to x and then a second time with respect to y. After integrating with x you will get a primitive function, let's call that one

which is a function of x and y. The integral of f between

and

will be

. Now you integrate this difference with respect to y. The function

appears two times in the expression, using two different x values, but integrate it once for an arbitrary value of x to get a primitive function

of

, which only depends on x and y (instead of a function depending on

,

and y). Since F is the primitive function of

, the primitive function of

will be

. Now, this is the moment when you insert your limits for y, to get the integral between

and

. After doing that, your expression will look like

I guess this is the expression you are looking for. Note however that this only works when you have a rectangular surface in the xy-plane with sides parallel to the x and y axes, over which you want to integrate. For other shapes, you will have to find other expressions.