Example: Evaluate , where
Solution: This function looks like this:
We have to decide on partitions. Note that in rectangles that do not involve
We look at the picture
and see that
The upper and lower sum can be also directly seen from the picture, the shaded area on the left is the upper sum, on the right the lower sum:
We therefore get bounds for infimum and supremum
This answer seems clear from the picture, the region consists of three squares of side one.