Don't listen to the guy above talking about integration. Integration is NOT the reversal of differentiation. That would be the anti-derivative. Integrals and anti-derivatives are NOT the same thing. But they are connected by the Fundamental Theorem of Calculus.
If a function f(x) has an anti-derivative F(x), the area under the curve from a to b is equal to F(b)-F(a).
This is integration defined.
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