Is the Set of Functions with a Zero Integral a Subspace of C[a,b]?

[jaredmt]

Homework Statement

Determine whether or not the given set is a subspace of the indicated vector space:
Functions f such that [integral from a to b]f(x)dx = 0; C[a,b]
(not sure how to do the coding for integrals)

Homework Equations

to be a subspace it must follow these axioms:
(i) if x and y are in W, then x + y is in W.
(ii) if x is in W and k is any scalar, then kx is in W.

The Attempt at a Solution

im having trouble understanding this. what exactly is C[a,b]?

 

[lanedance]

could it be the set of all continuous functions defined on [a,b]?

is there any more to the question?

 

[aPhilosopher]

0 + 0 = 0

c0 = 0 where c is an arbitrary constant.

Use properties of the integral.