  Let $A$ be a Koszul Artin-Schelter regular algebra with Nakayama automorphism
$\xi$. We show that the Yoneda Ext-algebra of the skew polynomial algebra
$A[z;\xi]$ is a trivial extension of a Frobenius algebra. Then we prove that
$A[z;\xi]$ is Calabi-Yau; and hence each Koszul Artin Schelter regular algebra
is a subalgebra of a Koszul Calabi-Yau algebra. A superpotential $\hat{w}$ is
also constructed so that the Calabi-Yau algebra $A[z;\xi]$ is isomorphic to the
derivation quotient of $\hat{w}$. The Calabi-Yau property of a skew polynomial
algebra with coefficients in a PBW-deformation of a Koszul Artin-Schelter
regular algebra is also discussed.
