How to calculate definite integral by definition?

How to calculate definite integral by definition?

If the integrand is f (x), the integral interval is (a, b)
If the integral region is divided into N parts and n tends to infinity, then the width of each small part is (B-A) / n
When each fraction is small enough, the integral area can be approximated as a rectangle, s = (B-A) / N * f (x)
Add up the area of these rectangles
I = 1 - > n (a-b) / N * f (a + (B-A) / N * I), which is the limit of finding the sum of the above formulas where n tends to infinity

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