Let $\phi, \psi : \mathbb{R} \rightarrow \mathbb{R}$ be step functions, with $\phi ≤ \psi$. Show that $\int{\phi} ≤ \int{\psi}$
I was thinking to convert it to a Riemann sum and show that the partitions of $\phi$ in [a,b] are less than $\psi$ in [c,d]?