JEE Math Practice Question

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 $${I_1} = \int\limits_0^{4nk} {f(x)dx} $$ and $${I_2} = \int\limits_{ - k}^{3k} {f(x)dx} $$, then :

1. A.$${I_1} + 2{I_2} = 4nk$$
2. B.$${I_1} + 2{I_2} = 2nk$$
3. C.$${I_1} + n{I_2} = 4{n^2}k$$
4. D.$${I_1} + n{I_2} = 6{n^2}k$$