A new model is presented for simulating coherent synchrotron radiation (CSR) in one dimension. The method is based on convolving an integrated Green function (IGF) with the longitudinal charge density. Since it is based on an IGF, the accuracy of this approach is determined by how well one resolves the charge density and not by resolving the single particle wake function. Since short-range wakefield effects are included analytically, the approach can be much more efficient than ordinary (non-IGF) approaches in situations where the wake function and charge density have disparate spatial scales. Two cases are presented: one derived from the full wake including short-range effects, and one derived from the asymptotic wake. In the latter case the algorithm contains the same physics as others based on the asymptotic approximation, but requires only the line charge density and not its derivative. Examples are presented that illustrate the limitations of the asymptotic-wake approximation, and that illustrate how microbunching can increase the CSR fields by orders of magnitude depending on the microbunching wavelength.