I was told this was a rather easy question, but I'm having troubles sorting it all out....

Given that $\displaystyle f$ is an integrable function on $\displaystyle [a,b]$, prove

1) For any $\displaystyle c>0$, $\displaystyle \int_{a}^{b}f(x)dx=c\int_{a/c}^{b/c}f(cx)dx$

2) For any $\displaystyle c\in\mathbb{R}$, $\displaystyle \int_{a}^{b}f(x)dx=\int_{a-c}^{b-c}f(x+c)dx$

The proof is said to be simplest by starting with the direct definitions of integrability.