## Riemann Integral

Suppose $\displaystyle f(x)$ is a continuous function on an interval$\displaystyle [0,1]$ except at a point $\displaystyle x_0 \in (0,1)$.If f is bounded on $\displaystyle [0,1]$. Using the definition of Riemann Integral, show that $\displaystyle f(x)$ is Riemann Integrable on $\displaystyle [0,1]$ and that $\displaystyle \int _0 ^1 f(x)dx$ is independent of the value $\displaystyle f(x_0)$.