Riemann Integral in terms of step function

Question

It is seen that, if $f(x)$ is a bounded real valued function, then $\displaystyle \overline{\int_a^b } f(x)\; dx= \inf \int_a^b \psi(x) dx \; $ where infimum is taken for all step functions $\psi(x)\ge f(x)$. Why we take all step functions $\; \psi(x)\ge f(x)$