A person walking along a straight path has her velocity in miles
per hour at time t given by the function v(t) = 0.25t^3 - 1.5t^2 + 3t +
0.25 , for times in the
interval 0 \leq t \leq 2 .
The graph of this function is also given in each of the three diagrams below.

Note that in each diagram, we use four rectangles to estimate the area under

Think about how the heights of the rectangles in the left-most diagram are
being chosen. Determine the value of

Use the rectangles in the middle diagram to find the value of

Use the rectangles in the right-most diagram to find the value of

Which estimate do you think is the best approximation of

In order to get credit for this problem all answers must be correct.