# Question #8be27

Supposing $f \left(x\right)$ continuous at ${x}_{0}$
${\lim}_{\delta \to 0} \frac{1}{2 \delta} {\int}_{{x}_{0} - \delta}^{{x}_{0} + \delta} f \left(x\right) \mathrm{dx} = {\lim}_{\delta \to 0} \frac{F \left({x}_{0} + \delta\right) - F \left({x}_{0} - \delta\right)}{\left({x}_{0} + \delta\right) - \left({x}_{0} - \delta\right)} = f \left({x}_{0}\right)$