Consider the function f(x) = 2x 3 2x 2 + x on the interval [0, 4].

(a) Evaluate the Riemann sum for this function with eight subintervals of equal width, taking the sample points to be the right endpoints.

(b) Evaluate the Riemann sum for this function with eight subintervals of equal width, taking the sample points to be the left endpoints.

(c) write down a limit which represents the area under the graph of f(x) from 0 to

4.

(d) ) Evaluate the limit from part 1(c). Please do not use The Evaluation Theorem or The Fundamental Theorem of Calculus.