The definite integral of a continues function like f(x) can be approximated by the sum of all narrow and tall rectangles areas obtained from partitioning [a,b] interval into n equal sub intervals each with a length of 
as shown in the figure. As n moves to a bigger number,the heights of each
rectangle would be a better approximation of the function values which results in a better area approximation, less error.
By approaching to infinity for n, the rectangles heights would be a perfect match to the whole function and results in the exact area bounded by the function and x-axis from x=a to x=b.
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