  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.
