Higher-order superintegrability of a Holt related potential

In a recent paper, Post and Winternitz (2011 J. Phys. A: Math. Theor. 44 162001) studied the properties of two-dimensional Euclidean potentials that are linear in one of the two Cartesian variables. In particular, they proved the existence of a potential endowed with an integral of third order and an integral of fourth order. In this paper we show that these results can be obtained in a more simple and direct way by noting that this potential is directly related to the Holt potential. It is proved that the existence of a potential with higher-order superintegrability is a direct consequence of the integrability of the family of Holt type potentials.