a) Use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval; b) Use the fundamental theorem of calculus to verify your result c) Find the average value of the function over the given interval. f(x)=3x2+2x+1, [1,4]   I'd like to know how to do part B

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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.