A new method of estimating the optical constants of thin films has been developed and applied to YBa2Cu3O7-x epitaxial single-crystal thin films (T-e = 90 K) grown on MgO substrates to determine the far-infrared optical conductivity sigma (ab)(Co), which is the response when an unpolarized excitation is applied parallel to the ab-plane in multidomain (twinned) single crystals of YBa2Cu3O7-x. In this method, both the transmittance spectra T(omega) and reflectance spectra R(omega) are measured as a function of the wave number w, and the results are substituted into a set of coupled equations which exactly describe R(omega) and T(omega) of thin films on substrates, where the complex refractive index N = n + ik of the thin films is an unknown parameter. The coupled equations are numerically solved using the Newton method, and the values of n and k are determined as a function of omega. We have determined sigma (ab)(omega) of YBa2Cu3O7-x thin films for w = 50-250 cm(-1) at T = 34-97 K. Analysis of the temperature dependence of sigma (ab)(omega) based on the two-fluid model suggests that the symmetry of the superconducting pairing state of the specimen is d-wave.