Regularization theorem :$ AC[0,1]$ to $\mathcal{C}^1[0,1]$

Question

For a given absolutely continuous function $x\in AC([0,1],\mathbb{R}^d)$ i.e : there is $f\in L^1[0,1]$ such that : $$x(t)= x(0)+ \int_0^tf(s)ds.$$ Can I find a continuously differentiable $y$, such that $y=x$ almost everywhere.

I was wondering if there is a regularization theorem.