**Statements of Theorems**

*Fundamental theorem of calculus.*Let*f*be a continuous real-valued function defined on a closed interval . Let*F*be the function defined, for all*x*in, by

Then, *F* is continuous on, differentiable on the open interval (*a*, *b*), and

for all *x* in (*a*, *b*).

*Second fundamental theorem of calculus*. Let*f*be a real-valued function defined on a closed interval that admits an antiderivative*g*on . That is,*f*and*g*are functions such that for all*x*in ,

If *f* is integrable on then

Read more about this topic: Integral, Fundamental Theorem of Calculus

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“In so far as the *statements* of geometry speak about reality, they are not certain, and in so far as they are certain, they do not speak about reality.”

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