- #1

- 3

- 0

**analysis proof...showing discontinuous function is integrable?**

## Homework Statement

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)

## Homework Equations

## 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]

Last edited: