Consider a parameterized curve $ C: x \equal{} e^{ \minus{} t}\cos t,\ y \equal{} e^{ \minus{} t}\sin t\ \left(0\leq t\leq \frac {\pi}{2}\right).$

(1) Find the length $ L$ of $ C$.

(2) Find the area $ S$ of the region bounded by $ C$, the $ x$ axis and $ y$ axis.

You may not use the formula $ \boxed{\int_a^b \frac {1}{2}r(\theta)^2d\theta }$ here.