We present the analytical calculation of the contribution of order
m_q^2 \alpha_s^4 n_f^2 to the absorptive part of the vacuum
polarization function of vector currents. This term constitutes an
important gauge-invariant part of the full O(m_q^2 alpha_s^4)
correction to the total cross-section of e^+ e^- annihilation into
hadrons. The results are compared to predictions following from
various optimization schemes.