  The International Gamma-Ray Astrophysics Laboratory (INTEGRAL) satellite has
yielded unprecedented measurements of the soft gamma-ray spectrum of our
Galaxy. Here we use those measurements to set constraints on dark matter (DM)
that decays or annihilates into photons with energies $E\approx 0.02-2$ MeV.
First, we revisit the constraints on particle DM that decays or annihilates to
photon pairs. In particular, for decaying DM, we find that previous limits were
overstated by roughly an order of magnitude. Our new, conservative analysis
finds that the DM lifetime must satisfy $\tau\gtrsim 5\times 10^{26}\,{\rm
s}\times (m_{\chi}/\rm MeV)^{-1}$ for DM masses $m_{\chi}=0.054-3.6$ MeV. For
MeV-scale DM that annihilates into photons INTEGRAL sets the strongest
constraints to date. Second, we target ultralight primordial black holes (PBHs)
through their Hawking radiation. This makes them appear as decaying DM with a
photon spectrum peaking at $E\approx 5.77/(8\pi G M_{\rm PBH})$, for a PBH of
mass $M_{\rm PBH}$. We use the INTEGRAL data to demonstrate that, at 95\% C.L.,
PBHs with masses less than $1.2\times 10^{17}$ g cannot comprise all of the DM,
setting the tightest bound to date on ultralight PBHs.
