The formulation of the problem of obtaining a unique integral function approximation to a real-valued locally analytic function is given. The integral function in this case is derived from an inhomogeneous, linear differential equation. A careful distinction is made between the approximation of the integral form which defines the polynomial coefficients of the differential equation which defines the integral function, and the approximation by the integral function itself. This formulation enables us to obtain results for existence, uniqueness and order of approximation in both normal and non-normal cases.