Definite integrals of piecewise functions

$f(x) = \begin{cases} \cos(x) & \text{for} ~~~~x\lt0 \\ 1-2x & \text{for} ~~~~ x \geq0\end{cases}$ **Evaluate the definite integral.** $\displaystyle\int^1_{-\frac{\pi}2}f(x)\,dx = $ [[☃ radio 1]]