I have been trying to tackle this question, and although I think I've found the answer, it seems either too obvious or I'm understanding the question incorrectly.
It goes as follows:
"Find the area of the region that lies under the graph f(x) = x between [0,2] by taking the limit of the sum of approximating rectangles whose heights are the values of the function at the right end point of each interval.
Included is a graph with 6 rectangles.
Now, if you just look at the darn thing, it's easy to see that the area under the graph would be 2 (because it's a right angle triangle). However, using the method asked (if I understood this correctly), I took the sum of the areas of each rectangle (so, each rectangle would be width=1/3, and height=f(x)) to which I got 7/3. Then it asked to take the limit of that number, which is a constant, so it would just be 7/3.
So am I missing something extremely obvious here?