If [tex]\int _{-\infty} ^{\infty}f(x)\: dx[/tex] is convergent and [tex]a[/tex] and [tex]b[/tex] are real numbers, show that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int _{-\infty} ^a f(x)\: dx + \int _a ^{\infty}f(x)\: dx = \int _{-\infty} ^b f(x)\: dx + \int _b ^{\infty}f(x)\: dx[/tex]

I'm clueless on how to show it other than by drawing what is stated: a generic finite integral being split into two finite pieces for each arbitrary point. Is there any other way to approach this problem?

Thanks

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# Improper integrals

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