$s(t) = |\sum_{n=1}^{\infty} \int_{0}^{t} u_{n}(x) dx|^{2}$ is a polynomial

Question

Let $\{u_{n}\}_{n \in \mathbb{N}}$ be an orthonormal subset of $L^{2}[0,1]$. Prove that the function $$s(t) =\left| \sum_{n=1}^{\infty} \int_{0}^{t} u_{n}(x) dx\right|^{2}$$

is a restriction of a polynomial by determinating such polynomial.

Any help would be appreciated.