Approximate with Riemann sum

Approximate Intergral [0,50] v(t)dt with a Riemann sum, using the midpoints of five subintervals of equal length. Using the correct units, explain the meaning of this integral.

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this is the table

t ----------------------v(t)
(seconds) ---- (feet per second)
0 ---------------------- 0
5 --------------------- 12
10 -------------------- 20
15 -------------------- 30
20 -------------------- 55
25 -------------------- 70
30 -------------------- 78
35 -------------------- 81
40 -------------------- 75
45 -------------------- 60
50 -------------------- 72

Please help. I am soo confused. 10 points!

Cutting [0, 50] into five subintervals of equal length means that each interval will have length

Δt = (50 - 0)/10 = 5.

The midpoint of the interval [0, 10] is at 5; the midpoint of [10, 20] is 15, and so forth.

50
∫ v(t) dt ≈ v(5) Δt, + v(15) Δt + v(25) Δt + v(35) Δt + v(45) Δt =
0

= 12(5) + 30(5) + 70(5) + 81(5) + 60(5) = 1265.

Notice that v(t) is in feet/sec and Δt is in sec. So each term has units of feet.

If v(t) is the velocity of an object moving along a straight line at the time t, then the above integral is the total distance traveled in 50 seconds.