Show that W = {ƒ∈D[-1,1] : ∫[-1,1]ƒ(x)dx = 0} is a subspace of D[-1,1].

Let D[-1,1] denote the space of all continuous functions ƒ : [-1,1] -> R, with the usual rules of function addition and scalar multiplication: for any ƒ, g ∈ D[-1,1] and λ ∈ R,

(ƒ + g)(x) = ƒ(x) + g(x), (λƒ)(x) = λƒ(x), for all x ∈ [-1,1]

D[-1,1] is a vector space.

Show that W = {ƒ∈D[-1,1] : ∫[-1,1]ƒ(x)dx = 0} is a subspace of D[-1,1].

I really need some help here. Thanks.