Doubt about solution of integration identity.

how this solution has taken? what I marked in question. they are not taking isinx terms. but they use simple sinx terms, if they are using expansion of e^imx and e^inx.OR what they did in this question. please tell. in attached file, all the solutions are present of all kind of equations. what they used? All in all, please show me by solving they did in this equation?