We employ neutron spherical polarimetry to determine the nature and population of the coexisting antiferromagnetic domains in multiferroic YMn2O5. By applying an electric field, we prove that reversing the electrical polarization results in the population inversion of two types of in-plane domains, related to each other by inversion. Our results are completely consistent with the exchange striction mechanism of ferroelectricity, and support a unified model where cycloidal ordering is induced by coupling to the main magnetic order parameter.