I am able to calculate $\int_{0}^{\infty} f(x) \cos(x)\, \mathrm{d}x$ for $f(x)$ being even by taking the real part of Complex Fourier transform (at $\omega = 1$). The two-sided sine transform is $0$, as $f(x)$ is even.
Is there a way to calculate the one-sided integral $\int_{0}^{\infty} f(x) \sin(x) \,\mathrm{d}x$ from the complex fourier transform $\int_{-\infty}^{\infty} f(x) e^{i \omega x} \,\mathrm{d}x$ when $f(x)$ is even?