6(d). (4 points) Determine whether the following statement is True or False; if False, provide a justification explaining why it is incorrect. You will receive 4 points for a correct answer, a penalty of −4 points for an incorrect answer, or 0 points for no answer.

If $f = \cos^2 x$, $g = \sin^2 x$, and $h = 1+x^2$, then $h$ lies in the space spanned by $f$ and $g$.