  The paper studies integral functionals with non-smooth functions from L_2
defined on solutions of ODEs. Some regularity is obtained in the form of
estimates of L_2-norm for these functionals. This result is used for
regularization of optimal control problems for ODEs with non-smooth
functionals: it is suggested to replace the initial vector by a random vector
with density. Necessary conditions of optimality and sufficient conditions of
existence of optimal control are obtained.
