The Ultraviolet Imaging Telescope (UVIT) on board the AstroSat observatory has imaged the Andromeda galaxy (M31) from 2017 to 2019 in the far- and near-UV (FUV and NUV) with the high spatial resolution of ≃1″. The survey covered the large sky area of M31 with a set of observations (Fields), each 28' in diameter. Field 1 was observed in two epochs with the F148W filter, separated by ≃1133 days (≃3.10 yr). The 6.4 kpc diameter Field 1 (at the distance of M31) includes a substantial part of the inner spiral arms of the galaxy. We identify UVIT sources in both epochs of Field 1 and obtain catalogs of sources that are variable in FUV at >3σ and >5σ confidence level. The fraction of FUV-variable sources is higher for brighter sources, and the fraction is higher in the two main spiral arms compared to other areas. This is evidence that a significant fraction of the FUV variables are associated with hot young stars. Source counterparts are found for 42 of the 86 >5σ FUV variables using existing catalogs. The counterparts include 10 star clusters, 6 H II regions, 5 regular or semiregular variables, 6 other variables, and 6 nova or nova candidates. The UVIT FUV-NUV and FUV-FUV color-magnitude diagrams confirm the association of most of the FUV variables with hot young stars. A catalog of UVIT photometry for the variable sources is presented.