Possible Duplicate:
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?
Possible Duplicate:
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?
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