  We prove space and time regularity for solutions of fully nonlinear parabolic
integro-differential equations with rough kernels. We consider parabolic
equations $u_t = \I u$, where $\I$ is translation invariant and elliptic with
respect to the class $\mathcal L_0(\sigma)$ of Caffarelli and Silvestre,
$\sigma\in(0,2)$ being the order of $\I$. We prove that if $u$ is a viscosity
solution in $B_1 \times (-1,0]$ which is merely bounded in $\R^n \times
(-1,0]$, then $u$ is $C^\beta$ in space and $C^{\beta/\sigma}$ in time in
$\overline{B_{1/2}} \times [-1/2,0]$, for all $\beta< \min\{\sigma,
1+\alpha\}$, where $\alpha>0$. Our proof combines a Liouville type theorem
---relaying on the nonlocal parabolic $C^\alpha$ estimate of Chang and
D\'avila--- and a blow up and compactness argument.
