Analysis - A bounded function with a finite number discontinuous on [a, b] is Riemann integrable

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A bounded function having a finite number of points of discontinuity on [a,b] is integral on [a, b]. A bounded function having a finite number of points of discontinuity on [a,b] is integral on [a, b].
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A bounded function with finitely many points of discontinuity is Riemann stieltjes integrable | Msc. A bounded function with finitely many points of discontinuity is Riemann stieltjes integrable | Msc.
theorem :- a bounded function with finite number of point of discontinuity is Riemann integral theorem :- a bounded function with finite number of point of discontinuity is Riemann integral
If f is bounded & has a finite no. of points of discontinuity on [a,b] then f is integrable on [a,b] If f is bounded & has a finite no. of points of discontinuity on [a,b] then f is integrable on [a,b]
Finite no of discontinuity function Riemann INTEGRABLE Finite no of discontinuity function Riemann INTEGRABLE