If I'm finding an area (using a Reiman sum) of the area under the graph of f(x)=1+x^2 between -1 and 2 using left end points and three rectangles (n=3) then I should get delta x = 1 and so the area using left end points is

f(x_0)+f(x_1)+f(x_2), which would be f(-1)+f(0)+f(1) => (1+(-1)^2) + (1+0) + (1+(1^2)) = 2 + 1 + 2 = 5

My text says it should be just over 6 using left end points, and 8 using right end points.

When I do it with the right and points I get an area of 8 => f(x_1) + f(x_2) + f(x_3) => (1+0) + (1+1) + (1+2^2) = 1+2+5 = 8