Is this operator compact in $L^2[0,d]$?

Question

Consider $X=L^2[0,d]$ and define $A \colon X \to X$ a linear bounded operator by the integral function \begin{equation} {A}x=\int_0^\cdot x(\xi)d\xi \end{equation} This operator looks compact to me since its range $R(A) \subset W^{1,2}$ which is continuously embedded with compact embedding into $X$. Is this true? How can I formalize the details?