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Study Stuff for MCA Examinations - NIMCET
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If $g$ is Riemann integrable on $[a,b]$ and $f(x)=g(x)$ except for a finite number of points in $[a,b]$, then
(a) $f$ is Riemann integrable and $\int_a^b f(x)\,dx=\int_a^b g(x)\,dx$
(b) $f$ is Riemann integrable and $\int_a^b f(x)\,dx<\int_a^b g(x)\,dx$
(a) $f$ is Riemann integrable and $\int_a^b f(x)\,dx=\int_a^b g(x)\,dx$
(b) $f$ is Riemann integrable and $\int_a^b f(x)\,dx<\int_a^b g(x)\,dx$
(c) $f$ is Riemann\text{-}integrable and $\int_a^b f(x)\,dx>\int_a^b g(x)\,dx$
(d) $f$ is not Riemann\text{-}integrable
(d) $f$ is not Riemann\text{-}integrable
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