Let f : R $ \to $ R be a continuous function such that f(x) + f(x + 1) = 2, for all x$\in$R. If ${I_1} = \int\limits_0^8 {f(x)dx} $ and ${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $, then the value of I1 + 2I2 is equal to ____________.

Question

Let f : R $ \to $ R be a continuous function such that f(x) + f(x + 1) = 2, for all x$\in$R.

If ${I_1} = \int\limits_0^8 {f(x)dx} $ and ${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $, then the value of I₁ + 2I₂ is equal to ____________.

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