Answer
$h(x)$ is in $span(f(x),g(x))$.
Work Step by Step
As $f(x)= \sin^{2}x$ and $g(x) = \cos^{2}x$, we have that
\begin{align*}
h(x) &= 1\\
&= \sin^{2}x + \cos^{2} x \\
&= 1\cdot \sin^{2}x + 1\cdot \cos^{2} x \\
&= 1\cdot f(x) + 1\cdot g(x)
\end{align*}
and clearly $1\cdot f(x) + 1\cdot g(x) \in span(f(x),g(x))$, so $h(x) \in span(f(x),g(x))$.
