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If $\displaystyle \int_{-\infty}^\infty f(x)\ dx$ is convergent and $a$ and $b$ are real numbers, show that$$\int_{-\infty}^a f(x)\ dx + \int_a^\infty f(x)\ dx = \int_{-\infty}^b f(x)\ dx + \int_b^\infty f(x)\ dx$$

$\int_{0}^{\infty} f(x) d x$

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Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Boston College

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