The covariant expressions are derived for the energy, momentum, and angular momentum of an arbitrary physical system of particles and vector fields acting on them. These expressions are based on the Lagrange function of the system, are the additive integrals of motion, and are conserved over time in closed systems. The angular momentum pseudotensor and the radius-vector of the system's center of momentum are determined in a covariant form. By integrating the motion equation over the volume the integral vector is calculated and the impossibility of treatment of the integral vector as the system's four-momentum is proved as opposed to how it is done in the general theory of relativity. In contrast to the system's four-momentum, which collectively characterizes the motion of the system's particles in the surrounding fields, the physical meaning of the integral vector consists in the taking account of all the energies and energy fluxes of the fields generated by the particles. The difference between the four-momentum and the integral vector is associated not only with the duality of particles and fields, but also with different transformation laws for four-vectors and four-tensors of second order. As a result, the integral vector turns out to be a pseudo vector of a special kind.