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## Homework Statement

If a<c<d<b and f is integrable on (a,b), show that f is integrable on (c,d)

## Homework Equations

## The Attempt at a Solution

I know that f is integrable on (a,b) iff for all e>0 there exists step functions g and h such that g [tex]\leq[/tex] f1

_{(a,b)}[tex]\leq[/tex] h and I(g-h) <e

( 1

_{(a,b)}in the indicator function and I(g-h) is the integral of the step functions)

I feel like this should allow me to fairly easily show that f is also integrable on (c,d) but I just don't know how to start.

Do I need to consider partitions?

Thanks.