Mathematics problems

These are simple questions:

Prove that for x is an integer:

[ (1/5) X^5 + (1/3) X^3 + (7/15) X  ] is also an integer.

and

1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ... - 2000^2 + 2001^2 = ...

You can answer it in the comment box...

thank you.