$[10$ points$]$ Complete these exercises about using Riemann sums and the definite integral.

Suppose that an object moving along a straight line path has it velocity in feet per second at time $t$ in seconds given by $v(t)=t^3+2.$

Express $M_3,$ the middle Riemann sum, for $v$ on $-1,5$ using sigma notation.

$M_3=2(0^3+2)+2(2^3+2)+2(4^3+2)$

Estimate the distance traveled on $-1,5$ by computing $R_3.$ Carefully illustrate the Riemann sum on the above graph, shading each rectangle.

Calculute the exact distance traveled on $-1,5$ by computing ${\displaystyle \underset{-1}{\overset{5}{}}}v(t)dt.$