A new perfectly matched layer (PML) formulation for the time domain finite element method is presented for Maxwell's equations. In particular, we focus on the time integration scheme which is based on Galerkin's method with a temporally piecewise linear expansion of the electric field. The time stepping scheme is constructed by forming a linear combination of exact and trapezoidal integration applied to the temporal weak form, which reduces to the well-known Newmark scheme in the case without PML. Extensive numerical tests on scattering from infinitely long metal cylinders in two dimensions show good accuracy and no signs of instabilities. For a circular cylinder, the proposed scheme indicates the expected second order convergence toward the analytic solution and gives less than 2% root-mean-square error in the bistatic radar cross section (RCS) for resolutions with more than ten points per wavelength. An ogival cylinder, which has sharp corners supporting field singularities, show similar accuracy in the monostatic RCS. The use of PML-techniques will also be demonstrated in the context of the shape optimization for various types of scatterers, where the objective is to minimize the RCS.