The rate of U.S. per capita sales of bottled water for the period 2007-2014 could be approximated by s(t) = 0.25t2 -t + 29 gallons per year (0 sts 7), where t is time in years since the start of 2007.t Use a definite integral to estimate the total U.S. per capita sales of bottled water from the start of 2009 to the start of 2012. (Round your answer to the nearest gallon.) gal

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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.