Let \( f : R \to R \) be a continuous function satisfying \( f(x) + f(x + k) = n \), for all \( x \in R \) where \( k > 0 \) and \( n \) is a positive integer. If \( I_{1} = \int_{0}^{4nk} f(x) \, dx \) and \( I_{2} = \int_{-k}^{3k} f(x) \, dx \), then:
