Erdős Problem #1131 — Minimum integrated squared Lagrange basis

For $x_1,\ldots,x_n\in [-1,1]$ let $l_k(x)=\frac{\prod_{i\neq k}(x-x_i)}{\prod_{i\neq k}(x_k-x_i)},$ which are such that $l_k(x_k)=1$ and $l_k(x_i)=0$ for $i\neq k$. What is the minimal value of $I(x_1,\ldots,x_n)=\int_{-1}^1 \sum_k \lvert l_k(x)\rvert^2\mathrm{d}x?$ In particular, is it true that $\min I =2-(1+o(1))\frac{1}{n}?$