Let f: R → R be a continuous function such that f(x)+f(x+1)=2, for all x ∈ R. If I_1=∫_0^8 f(x) d x and I_2=∫_-1^3 f(x) d x, then the value of I_1+2…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function such that $\displaystyle f(x)+f(x+1)=2$, for all $\displaystyle x \in \mathbf{R}$. If $\displaystyle \mathrm{I}_1=\int_0^8 f(x) \mathrm{d} x$ and $\displaystyle \mathrm{I}_2=\int_{-1}^3 f(x) \mathrm{d} x$, then the value of $\displaystyle \mathrm{I}_1+2 \mathrm{I}_2$ is equal to \_\_\_\_.