dfinite integration

If f(a-x)=-f(x), show that ∫(fx)dx [0,a] =0
f(a-x) = -f(x)
Integrate both side,
∫f(a-x)dx = -∫f(x)dx
-∫f(a-x)d(a-x) = -∫f(x)dx
∫f(a-x)d(a-x) = ∫f(x)dx

Let g(x) = ∫f(x)dx
g(a-x) = g(x)
Put x = a, g(a-a) = g(a) => g(a) = g(0)
Hence, ∫[0,a]f(x)dx = 0