Evaluate the following definite integrals using the Fundamental Theorem[s] of Calculus. (a) Evaluate

R 4 0 x2+4x+2 dx.

Which of the Riemann Sum estimations from the previous problem were overestimates, and which were underestimates? (b) Evaluate R 2 2 x3 dx.

Explain why the result, though initially strange, makes sense with respect to the graph of x

c) If h(x) = R x5 cos(x) + 3x4 dx, find h(x). 2

(d) If g(x) = R 4 2x3 /sin(3x + 2) dx, find g(x).