∫[a,b]f(x)dx=F(a)-F(b)

F(a+2π)-F(a)
=F(a)-F(a)
=0

F(2π)-F(0)
=F(0)-F(0)
=0

∴∫[a, a+2π] f(x)dx = ∫[0, 2π] f(x)dx