In this worksheet, we explore the Fundamental Theorem of Calculus and applications of the Area Problem to problems involving distance and velocity. We also consider integrals involving net and total change. Let f(x) be given by the graph to the right and define A(x) = ∫₀ˣ f(t) dt. Compute the following: A(1), A(2), A(3), A(4), A'(1), A'(2), A'(3), A'(4), the maximum and minimum values of A(x) on the interval [0, 5]. Also, for a toy car travelling on a straight track with velocity v(t), define s(t) as the position of the car in meters, and compute s(2), s(4), s(6), s(7), v(2), v(4), v(6), along with the maximum and minimum values of s(t) and v(t) on the interval [0, 7].