Integral of inverse functions

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Calculus
${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse ${\displaystyle f^{-1}}$ of a continuous and invertible function ${\displaystyle f}$, in terms of ${\displaystyle f^{-1}}$ and an antiderivative of ${\displaystyle f}$. This formula was published in 1905 by Charles-Ange Laisant.