(adsbygoogle = window.adsbygoogle || []).push({}); analysis proof...showing discontinuous function is integrable?

1. The problem statement, all variables and given/known data

if a function f : [a,b] is Riemann integrable and g :[a,b] is obtained by altering values of f at finite number of points, prove that g is Riemann integrable and that

∫ f = ∫ g (f and g integrated from a to b)

2. Relevant equations

3. The attempt at a solution

g is bounded on [a,b] so for all E>0 let Q be a partition of [a, b] such that

PcQ

then L(P,f)<L(Q,g)<U(Q,g)<U(P,f) (inequalities should be less than or equal

to...how to type that?)

therefore U(Q,g)-L(Q,g)<E

therefore g is Riemann integrable on [a,b]

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# Analysis proof showing discontinuous funtion is integrable?

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