We are concerned with the subdifferentials of integral functionals and functions given in the form E-f(x) = f(T) f (t, x)d mu, for a possibly nonconvex normal integrand f defined on a separable Banach with separable dual and a nonnegative sigma-finite measure mu. We establish some limit-based estimates for the Frechet and the limiting subdifferentials of E-f, covering the cases of Lipschitz and non-Lipschitz integrands.