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