What you are doing when forming a Reimann sum is approximating the area under a curve by breaking it up into subintervals, and then usie a rectangle (with a base length equal to the subinterval length and some height to best match the height of the curve in that subinterval). This rectangle then approximates the area under the curve in that particular subinterval. You then add up the areas of the rectangle from each subinterval to obtain your approximation.
The more subintervals you use, the smaller the base of each rectangle is, and the more accurate your approximation of the area under the curve over the whole interval is.
In your instance, you are told to use 5 fixed subintervals to evaluate the area under the curve v(t) from 0 to 50. Hence, your 5 subintervals are [0,10], [10,20], [20,30], [30,40], and [40,50]. You are further told to use the midpoint of each subinterval as the height for your rectangles.
Hence, your rectangle for the interval [0,10] has base length of 10, and a height of v(5), or 12. Hence, the area of this rectangle is 120. Using the units corresponding to your problem the base (time t) is measured in seconds, while the height (v(t)) is measure in feet per second-- so the 120 represents 120 seconds * feet/second, or 120 feet.
The rectangle for the interval [10,20] has base length of 10, and a height of v(15), or 30. Hence, the area of this rectangle is 300, which represents 300 feet.
Continue this for the other 3 intervals, add them up, and you end up with an approximation for the area under the curve v(t) from 0 to 50 (which is what the integral in Problem D represents). If you notice what the units of the area are, it should be obvious what the meaning of this integral are.