Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics electric and magnetic fields are mainly expressed in terms of integrals over charge and current distributions, relativistic transformations are traditionally applied to point charges and elementary currents. The purpose of this paper is to show that relativistic transformations can be easily applied to electromagnetic integrals and that relativistic transformation of such integrals constitutes a valuable method for solving a variety of electromagnetic problems involving moving electromagnetic system. Six illustrative examples on relativistic transformation of electromagnetic integrals, including transformation of Maxwell's equations in their integral form, are presented in this paper.