Fundamental Theorem of Calculus

1. 1. An antiderivative of a function $f$ is one function $F$ whose derivative is $f$.

      OR

      $F(x)$ is the antiderivative of $f(x)$

      For example:

      

       

 

1. A definite integral equals the difference between the antiderivative of the bounds of the definite integral

$$F(b) - F(a) = \int_{c}^{b} f(t)\,dt - \int_{c}^{a} f(t)\,dt = \int_{a}^{b} f(t)\,dt$$

 

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