M2, M3. Suppose that the velocity of a moving object is given by v(t) = (t - 1)(t - 3)(t - 6). (a) Write down an expression in terms of definite integrals that describes the total distance traveled by the object over the interval [0, 8]. (b) Write down an expression in terms of definite integrals that describes the total change in position of the object over the interval [0, 8]. (c) Estimate the total change in position of the object over the interval [0, 8] using a midpoint Riemann sum with 4 subintervals. (Your solution should probably involve a picture!) (d) Building on your solution for part (c), express the total change in position of the object over the interval [0, 8] as a limit of Riemann sums. (Note: You don't need to actually evaluate this limit!)