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Why is the area under a curve the integral?
Why does calculating an integral or an anti-derivatives represent an area? How do they figure it out? What is the relationship between them?
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A textbook on calculus will have some explanation and intuitive motivation for this. – GEdgar Jul 13 '12 at 23:30
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This is basic level stuff covered in first course of calculus. You may also refer to this:
http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Geometric_intuition
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