The limit $$\underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}} x_i \sin(x_i) \Delta x$$ can be expressed as a definite integral on the interval $[0,\pi]$ of the form $$\int_{a}^{\,b} {f(x)}\, dx$$ Determine $a, b,$ and $f(x)$.

$a =$

$b =$

$f(x) =$