  We present a new method of quantifying a galaxy's accretion history from its
integrated spectrum alone. Using full spectral fitting and calibrated
regularization techniques we show how we can accurately derive a galaxy's mass
distribution in age-metallicity space and further separate this into stellar
populations from different chemical enrichment histories. By exploiting the
fact that accreted lower mass galaxies will exhibit an offset to lower
metallicities at fixed age compared to the in-situ stellar population, we
quantify the fraction of light that comes from past merger events, that are
long since mixed in phase-space and otherwise indistinguishable. Empirical
age-metallicity relations (AMRs) parameterized for different galaxy masses are
used to identify the accreted stellar populations and link them back to the
progenitor galaxy's stellar mass. This allows us to not only measure the host
galaxy's total ex-situ mass fraction ($f_{acc}$), but also quantify the
relative amount of accreted material deposited by satellite galaxies of
different masses, i.e. the accreted satellite mass function in analogy to the
subhalo mass function. Using mock spectra of simulated, present-day galaxies
from the EAGLE suite we demonstrate that our method can recover the total
accreted fraction to within $\approx 12 \%$, the stellar mass of the most
massive accreted subhalo to within $\approx 26 \%$ and the slope of the
accreted satellite mass function to within $\approx 16 \%$ of the true values
from the EAGLE merger trees. Future application of this method to observations
could potentially provide us accretion histories of hundreds of individual
galaxies, for which deep integrated light spectroscopy is available.
