An integral $I$ over a counterclockwise circle $\textbf{C}$ is given by $$I=\oint _c \frac{z^2-1}{z^2+1} e^z dz.$$ If $\textbf{C}$ is defined as$\mid z \mid=3$ , then the value of* *$I$ is

- $-\pi i \sin(1)$
- $- 2\pi i \sin(1)$
- $-3\pi i \sin(1)$
- $-4\pi i \sin(1)$