In Exercises 35 and 36 of the section on Area and the Definite Integral, you calculated the distance that a car traveled by estimating the integral ∫₀^T v(t) dt.

(a) Let s(t) represent the mileage reading on the odometer. Express the distance traveled between t = 0 and t = T using the function s(t).    

(b) Since your answer to part (a) and the original integral both represent the distance traveled by the car, the two can be set equal. Explain why the resulting equation is a statement of the Fundamental Theorem of Calculus.