  This paper is devoted to the study of the expected-integral multifunctions
given in the form \begin{equation*}
\operatorname{E}_\Phi(x):=\int_T\Phi_t(x)d\mu, \end{equation*} where
$\Phi\colon T\times\mathbb{R}^n \rightrightarrows \mathbb{R}^m$ is a set-valued
mapping on a measure space $(T,\mathcal{A},\mu)$. Such multifunctions appear in
applications to stochastic programming, which require developing efficient
calculus rules of generalized differentiation. Major calculus rules are
developed in this paper for coderivatives of multifunctions
$\operatorname{E}_\Phi$ and second-order subdifferentials of the corresponding
expected-integral functionals with applications to constraint systems arising
in stochastic programming. The paper is self-contained with presenting in the
preliminaries some needed results on sequential first-order subdifferential
calculus of expected-integral functionals taken from the first paper of this
series.
