I want to show that $\underline{\int_{a}^{b}} f \ d \alpha \leq \overline{\int_{a}^{b}} f \ d \alpha$
So I want to show that $\sup L(P,f, \alpha) \leq \inf \ U(P, f, \alpha)$. Can I just suppose that $\sup L(P,f, \alpha)> \inf \ U(P, f, \alpha)$ and come up with a contradiction?