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We have used optical observations of resolved stars from the PanchromaticHubble Andromeda Treasury (PHAT) to measure the recent (< 500 Myr) starformation histories (SFHs) of 33 FUV-bright regions in M31. The region areasranged from ~$10^4$ to $10^6$ pc$^2$, which allowed us to test the reliabilityof FUV flux as a tracer of recent star formation on sub-kpc scales. The starformation rates (SFRs) derived from the extinction-corrected observed FUVfluxes were, on average, consistent with the 100-Myr mean SFRs of the SFHs towithin the 1$\sigma$ scatter. Overall, the scatter was larger than theuncertainties in the SFRs and particularly evident among the smallest regions.The scatter was consistent with an even combination of discrete sampling of theinitial mass function and high variability in the SFHs. This resultdemonstrates the importance of satisfying both the full-IMF and theconstant-SFR assumptions for obtaining precise SFR estimates from FUV flux.Assuming a robust FUV extinction correction, we estimate that a factor of 2.5uncertainty can be expected in FUV-based SFRs for regions smaller than $10^5$pc$^2$, or a few hundred pc. We also examined ages and masses derived from UVflux under the common assumption that the regions are simple stellarpopulations (SSPs). The SFHs showed that most of the regions are not SSPs, andthe age and mass estimates were correspondingly discrepant from the SFHs. Forthose regions with SSP-like SFHs, we found mean discrepancies of 10 Myr in ageand a factor of 3 to 4 in mass. It was not possible to distinguish the SSP-likeregions from the others based on integrated FUV flux.

The Panchromatic Hubble Andromeda Treasury. VI. The reliability of far-ultraviolet flux as a star formation tracer on sub-kpc scales