This subsection of bookofproofs.org is dedicated to the Riemann integral, which is defined on some closed real intervals $[a,b]$. The Riemann integral $\int_a^b f(x)dx$ can be interpreted as the area enclosed by the $x$-axis and the graph of the function $f$ on the interval $[a,b]$.
In some sense, the integration is inverse to the differentiation, which is shown in the corresponding theorem. This fact allows in many cases to calculate the integral of a function using an explicit formula.
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