probability - Let $F_X(x):=P(Xleq x)$ a distribution function of a random variable $X$. Prove that $F_X$ is right-continuous.

Let $F_X(x):=P(X\leq x)$ a distribution function of a random variable $X$.

Prove that $F_X$ is right-continuous.

I need to show that for every non-increasing sequence $x_n$ with $\lim x_n=x$ I will get:

$$\lim_{n\to\infty}f(x_n)=f(x_0)$$

How do I show this ? Any ideas ?