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fundamental theorem of calculus

A theorem in calculus with two results.

Part 1:

\frac{d}{d x} \int_{a}^{x} f (t) d t = f (x)

$\frac{d}{d x} \int_{a}^{x} f (t) d t = f (x)$

Part 2:

\int_{a}^{b} f (x) d x = F (b) - F a

$\int_{a}^{b} f (x) d x = F (b) - F a$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$