An essential improvement is given of a recent existence result of Crasta [G. Crasta, SIAM J. Control Optim., 38 (1999), pp. 237-253] for a nonconvex, noncoercive variational problem whose integrand does not depend on the state variable. This is shown to follow by the methods based on Fatou's lemma in several dimensions of [E. J. Balder, J. Math. Anal. Appl., 101 (1984), pp. 527-539]. The associated Euler Lagrange inclusions follow from well-known optimality conditions for such problems [V. M. Alekseev, V. M. Tichimirov, and S. V. Fomin, Optimal Control, Consultants Bureau, New York, 1987; V. I. Arkin and V. L. Levin, Uspekhi Mat. Nauk, 27 (1972), pp. 21-77].