There has a significant development in impulsive theory especially in the area of impulsive differential equations with fixed moments; see for instance the monographs [1-4] the references therein. In this paper, we study existence and uniqueness of nonlinear impulsive differential equations of the type for a.e. ,
subject to two-point and integral boundary conditions , and impulsive conditions , where is given matrices, ; and , are given function; , and are the right and left hand limits of at , respectively. The sufficient conditions are established for the existence of solutions for a class of two-point and integral boundary value problems for impulsive differential equations.

In the work the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. By the help of Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.