  We have used optical observations of resolved stars from the Panchromatic
Hubble Andromeda Treasury (PHAT) to measure the recent (< 500 Myr) star
formation histories (SFHs) of 33 FUV-bright regions in M31. The region areas
ranged from ~$10^4$ to $10^6$ pc$^2$, which allowed us to test the reliability
of FUV flux as a tracer of recent star formation on sub-kpc scales. The star
formation rates (SFRs) derived from the extinction-corrected observed FUV
fluxes were, on average, consistent with the 100-Myr mean SFRs of the SFHs to
within the 1$\sigma$ scatter. Overall, the scatter was larger than the
uncertainties in the SFRs and particularly evident among the smallest regions.
The scatter was consistent with an even combination of discrete sampling of the
initial mass function and high variability in the SFHs. This result
demonstrates the importance of satisfying both the full-IMF and the
constant-SFR assumptions for obtaining precise SFR estimates from FUV flux.
Assuming a robust FUV extinction correction, we estimate that a factor of 2.5
uncertainty 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 UV
flux under the common assumption that the regions are simple stellar
populations (SSPs). The SFHs showed that most of the regions are not SSPs, and
the age and mass estimates were correspondingly discrepant from the SFHs. For
those regions with SSP-like SFHs, we found mean discrepancies of 10 Myr in age
and a factor of 3 to 4 in mass. It was not possible to distinguish the SSP-like
regions from the others based on integrated FUV flux.
