Definite integral of a function f(x) from x=a to x=b w.r.t. x represent area under the 
curve from x=a to x=b as shown in the figure.
The area under the curve can be divided into rectangular regions but the area under the curve will not be exactly equals to sum of areas of rectangles. If we increase the number of rectangles the area will become closer and closer to the area under the curve. If the number of rectangles are taken sufficiently large i.e. approaches infinity such that the width of each rectangle approaches zero, the area under the curve becomes approximately equals to sum of areas of rectangles.
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