$x_{cm} = 0$ because of symmetry about the $y-$axis

$y_{cm} = \cfrac{\int ydm}{\int dm}$

$dm = \sigma r \alpha dr$

$y_{cm} = \cfrac{\int_0^R r \cfrac{\sin (\alpha /2)}{\alpha /2} r \alpha dr}{\int_0^R r \alpha dr}$

$=\cfrac{2}{3} R \cfrac{\sin (\alpha /2)}{(\alpha /2)}$