Evaluate $\int_0^9f(x)$ dx,where f(x) is defined by $f(x)=\left\{\begin{array}{1 1}\sin x;if 0\leq x\leq \large\frac{\pi}{2}\\1;\large\frac{\pi}{2}\normalsize\leq x\leq 5\\e^{x-5};5\leq x\leq 9\end{array}\right.$

Question

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com