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integral

Given a function $f (x)$ of a real variable $x$ and an interval $[a, b]$ of the real line, the integral $\int_{a}^{b} f (x) d x$ is equal to the area of a region in the xy-plane bounded by the graph of $f$ , the x-axis, and the vertical lines $x = a$ and $x = b$ , with areas below the x-axis being subtracted.

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