The velocity, f(t) in ft /sec, of an object at time t seconds is given in the table below. 1 2 3 4 5 6 f(t) 5 6 8 12 15 a. Use the right hand Riemann sum to estimate the distance the object traveled from time t =0 to t=6, use At = 2. b. Use the left hand Riemann sum to estimate the distance the object traveled from time t =0 to t =6, use At = 2. c. Assume the velocity of the object was strictly increasing, give an estimate of how far do you think the object actually traveled over this six second interval of time? Give a specific number for your answer; do not give an interval answer. Give a clear reason for your answer.

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.