(a) Consider the integral $\displaystyle \int_{0}^{\,\pi} {\sin(5x)}\,dx.$ Which of the following expressions represents the integral as a limit of Riemann sums?

A. $\displaystyle \underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}}\, \frac{\pi}{n} \, \sin\left(\frac{\pi i}{n}\right)$
B. $\displaystyle \underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}}\, \sin\left(\frac{\pi i}{n}\right)$
C. $\displaystyle \underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}}\, \frac{\pi}{n} \, \sin\left(\frac{5\pi i}{n}\right)$
D. $\displaystyle \underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}}\, \frac{\pi}{n} \, \sin\left(\pi+\frac{5\pi i}{n}\right)$
E. $\displaystyle \underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}}\, \sin\left(\pi+\frac{5\pi i}{n}\right)$
F. $\displaystyle \underset{n \rightarrow \infty}{\lim} \overset{n}{\underset{i=1}{\sum}}\, \sin\left(\frac{5\pi i}{n}\right)$

(b) Use a computer algebra system to evaluate the limit in the correct answer to (a), thereby obtaining the value of the integral.

Value of integral =