I want to know why
$$\int_0^\infty \frac{\cos wx\sin w}{w}\,dw = \frac{\pi}{4}?$$ at x=0,given that $$\int_0^\infty \frac{\cos wx\sin w}{w}\,dw = \frac{\pi f(x)} {2}$$ where f(x) is \begin{cases} 1 & \quad \text{if } |x|<1\\ 0 & \quad \text{if } |x|>1\\ \end{cases}
