Proof of fourier transform expression

I want to split $ J= int_0^{infty} e^{ik_ax}f(x) dx$ into a real and imaginary part as follows:

$ J= int_0^{infty} e^{ik_ax}f(x) dx = frac{1}{2} widetilde{f}(k_a) +frac{1}{2pi i} mathcal{P}int_{-infty}^{infty} frac{widetilde{f}(k)}{k-k_a} dk $ , where $mathcal{P}$ denotes the Cauchy value of the integral and $widetilde{f}(k) $ is defined as the Fourier transform of $ f(x)$:
$widetilde{f}(k)= int_{-infty}^{infty} e^{ikx} f(x) dx $.

Does this identity have a name and how would one proof it?