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I know that integration is the inverse process of differentiation, and that the definite integral is defined as:

[itex]\int_{a}^{b} f(x) dx = \lim_{n \to \infty} \sum^{n}_{i = 1} f(x_i) \Delta x[/itex]

assuming that the integrand is defined over the interval [a,b].

My question is: Why is it that the antiderivatives give the area under the curve? For example:

[itex]\int \frac{1}{1+x^2} dx = \arctan{x} + C[/itex]

How does arctan give the area under curve of the integrand between a and b?

Thanks and much appreciated,

JinM

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# Integration is the inverse process of differentiation

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