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This paper presents a stable and accurate method to compute the electromagnetic scattering from homogeneous, isotropic, and nondispersive bodies using time-domain integral equations (TDIEs). Unlike previous TDIE-based scattering work, the formulation presented here is based on the equations of Poggio, Miller, Chang, Harrington, Wu, and Tsai formulation. The method employs the higher-order divergence-conforming basis functions described by Graglia et al. and bandlimited interpolation functions to effect the spatial and temporal discretization of the integral equations, respectively. As the temporal basis functions are noncausal, an extrapolation mechanism is used to modify the noncausal system of equations to a form solvable by standard marching-on-in-time procedure. This work also explains the reason for late-time low-frequency instabilities encountered in current TDIE implementations and details a stabilization technique employed to overcome them. Numerical results demonstrate the accuracy and stability of the proposed technique.