= Solution
The function $x^2-1$ is an <even function>, while every sine basis function is an <odd function>. Their product is odd, so every sine coefficient is zero:
$$
\langle x^2-1,\sin(nx)\rangle=0.
$$
The function itself is not zero, and therefore \b[it cannot be represented by this sine basis]. The basis spans the odd subspace, whereas the requested nonzero even function lies in its <orthogonal complement>. Equivalently, any pointwise limit of odd partial sums remains odd wherever both reflected points have limits.
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