1. The problem statement, all variables and given/known data There are 2 questions which deal with the concept of double integration. I think there's no need for any calculations, which might have been easier, in my opinion. 1. 2. http://img2.uploadhouse.com/fileuploads/17065/170654043ae9d827241bff097ca2ee9760242ef0.png 2. Relevant equations $$L_f(P)\leq I\leq U_f(P)$$ Example, for f(x,y)=x+y-2 3. The attempt at a solution 1. Given the condition that ##L_f(P) = U_f(P)##, i would say that the partition P of R, would need to be a point. Therefore, since R is a rectangle, i would say that f is a simple line (straight or curved) on that rectangle? Or is f just a point on that rectangle? I'm not sure how to visualize this problem. Is there a trick to understand this? 2. I'm not sure i even understand the first part about the original f being continuous. I try to imagine the original f as being a piece of string and the shape is irregular, as for the boundary of Ω. Then, stretch that irregular shape to fit into the rectangular shape, R. Is that a correct assumption? Do i need to consider this in terms of 3D?