$$X \overset f \longrightarrow S^n$$
$$\begin{array}{c} X \\ \small i \downarrow & \searrow \small f \\ S^n \setminus \{pt\} & \underset h \hookrightarrow S^n \\ \small {g^{-1}} \downarrow \small \sim \\ \Bbb R^n \end{array}$$
$$X \times I \longrightarrow \Bbb R^n \overset g {\underset \sim \longrightarrow} S^n \setminus \{pt\} \overset h \hookrightarrow S^n$$
I was trying to evaluate $ {\int_0^{\infty}\frac{\cos (x)}{1+x^2}}\text{d}x$ by Feynman's trick
It has been solved here, but I have a specific question at one of the steps while doing it. (Not a duplicate)
So I defined $I(t)= \int_0^{\infty}\frac{\cos (xt)}{1+x^2}\text{d}x$ and arrived at $I(t...
