In the description is my question

Question

When estimating distances from a table of velocity data, it is not necessary that the time intervals are equally spaced. After a space ship is launched, the following velocity data is obtained. Use these data to estimate the height above the Earth's surface at 117 seconds.

t (sec)v (ft/s)
0	0
7	154
17	374
21	462
47	1034
60	1320
64	1508
117	3999

(a) lower estimate of distance traveled =  miles

(b) upper estimate of distance traveled =  miles

Answer 1

Sketch it out and sketch in the "rectangles". The lower limit, in this case, is the left hand Reimann Sum and the upper limit is the right hand sum.

Here is a sketch of the left hand sum:

Then just multiply length times width to get the area of each rectangle and add them up. The distance is the area under the curve. Do the same for the right hand sum except the rectangles are all based off the right hand "dot".

When you get your sums, don't forget that you will need to convert feet to miles.