I'm hoping this problem hasn't been posted before. I couldn't find a similar problem in the search so I'm posting a new thread.

Right, the following question was giving to us in one of our worksheets:

Now I know that, in order to prove that a certain vector space (V) is a subspace of another vector space (H), you have to go through the following three axioms:

1) The zero vector of V is in H.

Is it true that ?
2) H is closed under vector addition.

Is it true that if then also ?
3) H is closed under scalar multiplication.

Is is true that if then also the definition field?

Tonio
The bit that's confusing me is the whole "integration" thing. I'm assuming the the range between -1 and 1 is reducing the size of the space of V... so am I supposed to integrate first or... I dunno, I just need general help with this problem.