Weierstrass approximation theorem

Let $f : [a,b] \to \mathbb{R}$ be a continuous function on a closed bounded interval $[a,b] \subset \mathbb{R}$. Then for every $\varepsilon > 0$, there exists a polynomial $P$ such that
$$\sup_{x \in [a,b]} |f(x) - P(x)| < \varepsilon.$$