# Riemann Integration Question

Ok, for any $\varepsilon>0$ you can find $r_0>0$ such that $\inf\{f(x):x\in B(x,r)\}\geq f(x_0)-\varepsilon$ and $\sup\{f(x):x\in B(x,r)\}\leq f(x_0)+\varepsilon$ for each $r. This allows you to get upper and lower estimates of the limit as close to $f(x_0)$ as you want.