  We present results for single pseudoscalar meson pole contributions and pion
box contributions to the hadronic light-by-light (LBL) correction of the muon's
anomalous magnetic moment. We follow the recently developed dispersive approach
to LBL, where these contributions are evaluated with intermediate mesons
on-shell. However, the space-like electromagnetic and transition form factors
are not determined from analytic continuation of time-like data, but directly
calculated within the functional approach to QCD using Dyson-Schwinger and
Bethe-Salpeter equations. This strategy allows for a systematic comparison with
a strictly dispersive treatment and also with recent results from lattice QCD.
Within error bars, we obtain excellent agreement for the pion electromagnetic
and transition form factor and the resulting contributions to LBL. In addition,
we present results for the $\eta$ and $\eta'$ pole contributions and discuss
the dynamical effects in the $\eta-\eta'$ mixing due to the strange quarks. Our
result for the total pseudoscalar pole contributions is $a_\mu^{\text{PS-pole}}
= 91.6 \,(1.9) \times 10^{-11}$ and for the pion-box contribution we obtain
$a_\mu^{\pi-\text{box}} = -16.3 \,(2)(4) \times 10^{-11}$.
