Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by v(t) = 1.1t2 − 2.6t + 2.3 million hours of video per year    (0 ≤ t ≤ 9), where t is time in years since June 2005.† Use a definite integral to estimate to the nearest million, the total number of hours of video uploaded from June 2010 to the June 2013.  million hours of video

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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.