Polynomial Ring is Generated by Indeterminate over Ground Ring

Theorem
Let $R$ be a commutative ring with unity.

Let $R[X]$ be a polynomial ring over $R$.

Let $\iota : R \to R[X]$ be the embedding.

Then $R[X]$ is generated by $X$ over $R$.

Proof
use Polynomial is Linear Combination of Monomials