Explicitly covariant form of the integral Maxwell equations

We analyze in detail the covariance of the integral forms of the Maxwell Equations. Different forms of writing the integral Maxwell equations in explicitly covariant form are analyzed. First, we show how one of these ways can be obtained from the differential Maxwell equations, both from their usual three vector form as from their covariant four vector form. Then we discuss how this covariant integral Maxwell equations can be obtained from usual integral Maxwell equations. We emphasize the necessity to write the usual integral equations without time derivatives. The integrations regions in the three-dimensional space and time are identified with parts of the same hyper-surface in four-dimensional space-time. This point is carefully analyzed. Later we discuss other forms of the integral Maxwell equations. We show how these new versions can be expressed in an explicitly covariant form.