Let denote the greatest integer that is smaller than or equal to x. Evaluate where D = {}.

Hints: The trick is to bring up the underlying region (which is a simple square) into two parts. D = D1 + D2

where

- D1 is the triangle with corners at (0,0), (1,0), and (0,1), excluding the diagonal from (0,1) to (1,0).
- D2 is the rest of the remaining region of D.

Therefore we have

= + .