  The dynamic conductivity \sigma(\omega) of graphene in the presence of
diagonal white noise disorder and quantizing magnetic field B is calculated. We
obtain analytic expressions for \sigma(\omega) in various parametric regimes
ranging from the quasiclassical Drude limit corresponding to strongly
overlapping Landau levels (LLs) to the extreme quantum limit where the
conductivity is determined by the optical selection rules of the clean
graphene. The nonequidistant LL spectrum of graphene renders its transport
characteristics quantitatively different from conventional 2D electron systems
with parabolic spectrum. Since the magnetooscillations in the semiclassical
density of states are anharmonic and are described by a quasi-continuum of
cyclotron frequencies, both the ac Shubnikov-de Haas oscillations and the
quantum corrections to \sigma(\omega) that survive to higher temperatures
manifest a slow beating on top of fast oscillations with the local
energy-dependent cyclotron frequency.Both types of quantum oscillations possess
nodes whose index scales as \omega^2. In the quantum regime of separated LLs,
we study both the cyclotron resonance transitions, which have a rich spectrum
due to the nonequidistant spectrum of LLs, and disorder-induced transitions
which violate the clean selection rules of graphene. We identify the strongest
disorder-induced transitions in recent magnetotransmission experiments. We also
compare the temperature- and chemical potential-dependence of \sigma(\omega) in
various frequency ranges from the dc limit allowing intra-LL transition only to
the universal high-frequency limit where the Landau quantization provides a
small B-dependent correction to the universal value of the interband
conductivity \sigma=e^2/4 \hbar of the clean graphene.
