Answer
$S$ is linearly independent set of vectors.
Work Step by Step
Consider the combination
$$a(x^2)+b(x^2+ 1) =0, \quad a,b \in R.$$
Which yields the following system of equations
\begin{align*}
a+b&=0\\
b &=0.
\end{align*}
It is clear that the above system has a unique solution; that is, the trivial solution,
$$a=0,\quad b=0.$$
Then, $S$ is linearly independent set of vectors.