The bounds you mentioned won't work because for example they include the point (x, y) = (2, 3) where x+y = 5 > 3. (I'm not being very careful to distinguish between and , etc., because it's not important for these kinds of problems, and the meaning should be clear.)

Geometrically the inequality x+y < 3 represents the region under the line x+y = 3 in the xy plane. So in D, this is the region under the diagonal going from the upper left to the lower right corner of the square.

Here's what I get: