The following table gives the the approximate amount of emissions, E, of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1940 and E = f(t). 1940 1950 1960 1970 1980|1990| 10 20 30 40 50 E 6.9 8.9 12.5 18.1 21.4 19.2 Estimate the integral: S f(t)dt = Be sure that you know what the units of your answer are, and what its meaning is! (Original data from the Statistical Abstract of the US, 1992)

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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.