Using the Bernoulli polynomials $(B_n)_{n \in \mathbb{N}}$ satisfying $B_n(z+1) - B_n(z) = nz^{n-1}$ for all $n \in \mathbb{N}^*$, deduce the expression of a polynomial function satisfying the equation $(E_h)$:
$$\forall x \in \mathbb{C},\, f(x+1) - f(x) = h(x)$$
on $\mathbb{C}$ when $h$ is a polynomial function.