Consider the following limit of Riemann sums of a function $f$ on $[a, b]$. Identify $f$ and express the limit as a definite integral. \[ \lim _{\Delta \rightarrow 0} \sum_{k=1}^{n} x_{k}^{*} \sin x_{k}^{*} \Delta x_{k} ;[2,3] \] The limit, expressed as a definite integral, is (Simplify your answers.)

Step 1 ：Consider the following limit of Riemann sums of a function \(f\) on \([a, b]\). Identify \(f\) and express the limit as a definite integral.

Step 2 ：\[\lim _{\Delta \rightarrow 0} \sum_{k=1}^{n} x_{k}^{*} \sin x_{k}^{*} \Delta x_{k} ;[2,3]\]

Step 3 ：The given limit is a Riemann sum for a function \(f(x) = x \sin x\) on the interval \([2, 3]\). The limit of this Riemann sum as the partition size goes to zero is the definite integral of the function over the interval.

Step 4 ：Therefore, the limit can be expressed as the definite integral of \(f(x) = x \sin x\) from 2 to 3.

Step 5 ：We can calculate the definite integral.

Step 6 ：\[\int_{2}^{3} x \sin x dx = -\sin(2) + 2\cos(2) + \sin(3) - 3\cos(3)\]

Step 7 ：\(\boxed{-\sin(2) + 2\cos(2) + \sin(3) - 3\cos(3)}\) is the final answer.