A new theory for temporal aberrations of dynamic optics by applying the direct integral method is put forward in the present paper. A new definition of temporal aberration is given, in which a certain initial energy of electron emission emitted from a photocathode along the axial direction was taken as a criterion. New expressions of the temporary aberration coefficients in integral forms for the electron optical imaging systems have been deduced. An electrostatic concentric spherical system model is used to test and verify expressions of the coefficients given by the ‘‘direct integral method’’ and ‘‘t variation method’’. The analytical solutions prove that both methods are correct and equivalent. Compared to the ‘‘t variation method’’, the direct integral method only needs to carry out the integral calculation for the three geometrical temporal aberration coefficients of the second order, which is more convenient and suitable for computation in the practical design. Finally, results of the study for the theory of temporal aberrations of electron optical imaging systems, from the point of view of methodology, have been elaborated.