Definition talk:Improper Integral

Is there any reason that $f$ is required to be continuous for all these definitions? I would think they'd apply even for discontinuous (but defined on the entire interval) functions, except possibly the unbounded ones. --CircuitCraft (talk) 19:06, 18 August 2023 (UTC)

If $f$ is discontinuous, you need to discuss its integrability. --Usagiop (talk) 19:59, 18 August 2023 (UTC)

I think we should discuss these things. It'll be pretty simple in this case though; the improper integral is defined if and only if all of the relevant Riemann integrals exist, and the limit exists. --CircuitCraft (talk) 20:17, 18 August 2023 (UTC)