By definition...
$ P(|Y| < \frac{1}{2}) \, = \int_{-\infty}^{\infty} f_Y (v) \, dv =\int_{-\frac{1}{2}}^{0} (1+v) \, dv + \int_{0}^{\frac{1}{2}} v \, dv = \frac{1}{2} $
