Let f(x) = sinx and g(x) - f(x) = f(4-x). What is ∫₀⁴ f(x)/g(x) dx equal to?

Let I = ∫₀⁴ f(x)/g(x) dx. Using property ∫₀^a F(x)dx = ∫₀^a F(a-x)dx: I = ∫₀⁴ f(4-x)/g(4-x) dx. Given g(x) = f(x) + f(4-x), so g(4-x) = f(4-x) + f(x) = g(x). Then I = ∫₀⁴ f(4-x)/g(x) dx. Adding: 2I = ∫₀⁴ [f(x) + f(4-x)]/g(x) dx = ∫₀⁴ g(x)/g(x) dx = ∫₀⁴ 1 dx = 4. So I = 2.