Question: Expanding multiple integral

Hi everyone,

I need to expand a sum inside a single multiple integral into separate integrals, as in:

  /                          /                  /
 |                          |                  |
 | (x y + y) dxdy =  | xy dxdy  +  | ydxdy   ,
 |                          |                  |             
/                          /                  /              

where x and y are not independent of each other.

What I've tried is:

> with(IntegrationTools);
> c3 := Int(Int(x*y+y, x), y);
                       /   /              
                      |   |               
                      |   |  (x y + y) dx dy
                      |   |               
                     /   /                
> Expand(c3);
         /  /          \  /  /     \      /  /        \  /  /       \
         | |           | | |        |    | |          | | |          |
         | |  x dx   | | |y dy  | + | |  1 dx  | | |  y dy  |   .
         | |           | | |        |    | |          | | |          |
         \/            /  \/       /      \/          /  \/         /

Also:

> with(IntegrationTools);

c3:=> Int(x*y+y, [x, y]);
                        /                
                       |                 
                       |  (x y + y) d[x, y]
                       |                 
                      /                  

> Expand(c3);
                /  /               \     /  /            \
                | |                 |    | |              |
              y | |  x d[x, y]  | + | |  y d[x, y] |
                | |                 |    | |              |
                \/                 /     \/              /
          
As you can see, the variables are treated as independent in the first case, while in the second y is actually pulled out of the integral altogether.

Is the problem that I need to state explicitly the relation between x and y (which I'd really prefer not to have to), or is there some more basic error?

Thanks!