Calculating sequence with integrals

Calculus Level pending

A sequence \(\{a_n\}\) is defined by \[a_n = \lim_{x \rightarrow 1} \frac{1}{x-1} \int^x_1 (t^2+n^2t)dt . \] Find \(\displaystyle\sum_{k=1}^{10} a_k .\)

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