Context. Accurate star formation histories (SFHs) of galaxies are fundamental for understanding the build-up of their stellar content. However, the most accurate SFHs - those obtained from colour-magnitude diagrams (CMDs) of resolved stars reaching the oldest main-sequence turnoffs (oMSTO) - are presently limited to a few systems in the Local Group. It is therefore crucial to determine the reliability and range of applicability of SFHs derived from integrated light spectroscopy, as this affects our understanding of unresolved galaxies from low to high redshift. Aims: We evaluate the reliability of current full spectral fitting techniques in deriving SFHs from integrated light spectroscopy by comparing SFHs from integrated spectra to those obtained from deep CMDs of resolved stars. Methods: We have obtained a high signal-to-noise (S/N ~ 36.3 per Å) integrated spectrum of a field in the bar of the Large Magellanic Cloud (LMC) using EFOSC2 at the 3.6-metre telescope at La Silla Observatory. For this same field, resolved stellar data reaching the oMSTO are available. We have compared the star formation rate (SFR) as a function of time and the age-metallicity relation (AMR) obtained from the integrated spectrum using STECKMAP, and the CMD using the IAC-star/MinnIAC/IAC-pop set of routines. For the sake of completeness we also use and discuss other synthesis codes (STARLIGHT and ULySS) to derive the SFR and AMR from the integrated LMC spectrum. Results: We find very good agreement (average differences ~4.1%) between the SFR (t) and the AMR obtained using STECKMAP on the integrated light spectrum, and the CMD analysis. STECKMAP minimizes the impact of the age-metallicity degeneracy and has the advantage of preferring smooth solutions to recover complex SFHs by means of a penalized χ2. We find that the use of single stellar populations (SSPs) to recover the stellar content, using for instance STARLIGHT or ULySS codes, hampers the reconstruction of the SFR (t) and AMR shapes, yielding larger discrepancies with respect to the CMD results. These discrepancies can be reduced if spectral templates based on known and complex SFHs are employed rather than SSPs. Based on observations obtained at the 3.6 m ESO telescope on La Silla (Chile) and with the Hubble Space Telescope, operated by NASA.Appendices are available in electronic form at http://www.aanda.org