Theorem. Let and be real valued functions that are Riemann integrable on . Then the following statements hold:
1. The function is Riemann integrable on and .
2. The function is Riemann integrable on the interval and .
3. The function is Riemann integrable on and .
Outline of Proof. The basic idea is that we basically look at and and show that they are in fact equal to those right hand sides?