Let $f: R \rightarrow R$ be continuous function satisfying $f(x)+f(x+k)=n$, for all $x \in R$ where $k>0$ and $n$ is a positive integer. If $I_1=\int_0^{4 n k} f(x) d x$ and $I_2=\int_{-k}^{3 k} f(x) d x$, then
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