Prove the metric space with the set of all real-coefficient polynomials restricted to [0,1] and the sup-metric is separable

Question

Prove $(Y,d)$ is separable. To clarify, a function $~f:[0,1]\to \mathbb{R}$ is an element of $Y$ if and only if $~f(x) = a_0 +\dotsc+a_{n}x^{n}$ for some $n\in\mathbb{N}\cup\{0\}$ and $a_0,\dotsc,a_n \in\mathbb{R}$.