  We perform atmospheric retrievals on the full optical to infrared ($0.3-5 \,
\mu \mathrm{m}$) transmission spectrum of the inflated hot Jupiter WASP-52b by
combining HST/STIS, WFC3 IR, and Spitzer/IRAC observations. As WASP-52 is an
active star which shows both out-of-transit photometric variability and
starspot crossings during transits, we account for the contribution of
non-occulted active regions in the retrieval. We recover a $0.1-10\times$ solar
atmospheric composition, in agreement with core accretion predictions for giant
planets, and a weak contribution of aerosols. We also obtain a $<3000$ K
temperature for the starspots, a measure which is likely affected by the models
used to fit instrumental effects in the transits, and a 5% starspot fractional
coverage, compatible with expectations for the host star's spectral type. Such
constraints on the planetary atmosphere and on the activity of its host star
will inform future JWST GTO observations of this target.
