A particle is travelling along a straight line from t = 0 to t = D seconds, and its acceleration is plotted in the figure below. On each of the intervals, [0, A], [A, B], [B, C] and [C, D], we apply one of the midpoint rule (Mn), the trapezoid rule (T), left Riemann sum (L.) or right Riemann sum (Rn). We can apply different methods on different intervals. a(1) A C D (a) Suppose you want to compute an upper bound for the displacement of the particle between t = 0 and t = D. By using one of Mn, Tn, Ln or Rn on each of the intervals, come up with a numerical scheme which guarantees we obtain an upper bound for the particles displacement between t = 0 and t = D. You should choose a combination which provides the best accuracy. Include justification for your choices. (b) Letting v(t) denote the velocity of the particle, suppose |"(t)| 3(1+t)e-for t [0, D] and (t)||2 cos(+)e for t [0, D]. Compute an upper bound for the error of our approximation of the displacement between [0, A] and [A, B] using n = 10 sub-intervals in each interval [0, A] and [A, B] respectively. The upper bounds can include A and B.