Question Number 136835 by mnjuly1970 last updated on 26/Mar/21
$$\:\:\:\:\:\:\:\:.....{nice}\:\:\:\:\:{calculus}... \\ $$$$\:\:\:{for}\:\:\:\:{f}\left({x}\right)={f}\left({x}+\pi\right)\:: \\ $$$$\:\:\:\:\:\int_{−\infty} ^{\:\infty} {f}\left({x}\right).\frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}\overset{{why}???} {=}\int_{\mathrm{0}} ^{\:\pi} {f}\left({x}\right){dx} \\ $$