For $p \in \mathbb{K}[X]$, express $Jp$ in terms of the derivatives $p^{(k)}$ ($k \in \mathbb{N}$) of $p$, where $J$ is defined by $Jp(x) = \int_x^{x+1} p(t)\,\mathrm{d}t$.
For $p \in \mathbb{K}[X]$, express $Jp$ in terms of the derivatives $p^{(k)}$ ($k \in \mathbb{N}$) of $p$, where $J$ is defined by $Jp(x) = \int_x^{x+1} p(t)\,\mathrm{d}t$.