A bounded function having a finite number of points of discontinuity on [a,b] is integral on [a, b].

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Analysis - A bounded function with a finite number discontinuous on [a, b] is Riemann integrable Analysis - A bounded function with a finite number discontinuous on [a, b] is Riemann integrable
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]
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.
Examples of set of points of discontinuity of a bounded function has finite number of limit points Examples of set of points of discontinuity of a bounded function has finite number of limit points
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
Theorem || Riemann Integral || Finite number of points of discontinuity Theorem || Riemann Integral || Finite number of points of discontinuity
Integrating Functions With Discontinuities II Properties Of Riemann Integration Integrating Functions With Discontinuities II Properties Of Riemann Integration
theorem :- if points of discontinuity has finite number of limit point then it Riemann integral theorem :- if points of discontinuity has finite number of limit point then it Riemann integral