  The star formation (SFH) and chemical enrichment (CEH) histories of Local
Group galaxies are traditionally studied by analyzing their resolved stellar
populations in a form of color-magnitude diagrams obtained with the Hubble
Space Telescope. Star clusters can be studied in integrated light using
ground-based telescopes to much larger distances. They represent snapshots of
chemical evolution of their host galaxy at different ages. Here we present a
simple theoretical framework for the chemical evolution based on the
instantaneous recycling approximation (IRA) model. We infer a CEH from a SFH
and vice versa using observational data. We also present a more advanced model
for the evolution of individual chemical elements which takes into account the
contribution of supernovae type Ia. We demonstrate that ages, iron and
$\alpha$-element abundances of 15 star clusters derived from fitting of their
integrated optical spectra reliably trace the CEH of the Large Magellanic Cloud
obtained from resolved stellar populations in the age range 40Myr$<t<$3.5Gyr.
The CEH predicted by our model from the global SFH of the LMC agrees remarkably
well with the observed cluster age-metallicity relation. Moreover, the present
day total gas mass of the LMC estimated by the IRA model ($6.2\cdot10^8
M_{\odot}$) matches within uncertainties the observed HI mass corrected for the
presence of molecular gas ($5.8\pm0.5\cdot10^8 M_{\odot}$). We briefly discuss
how our approach can be used to study SFHs of galaxies as distant as 10Mpc at
the level of detail that is currently available only in a handful of nearby
Milky Way satellites.
