Limit of sum of derivative quotients

Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by $$f(x)=x^2\sin(x-1) + x e^{x-1},\quad x\in\mathbb{R}.$$ Then, $$\lim_{n\to\infty} n\left(f\left(1+\frac{1}{n}\right) + f\left(1+\frac{2}{n}\right) + \dots + f\left(1+\frac{10}{n}\right) - 10\right)$$ equals __________