Let f be integrable over [0, a] for any real a. If we define ${\mathrm{I}}_1={\int }_0^{\mathrm{\pi }/2} \cos \theta f\left(\sin \mathrm{\theta }+{\cos }^2\mathrm{\theta }\right)\mathrm{d\theta }$ and ${\mathrm{I}}_2={\int }_0^{\mathrm{\pi }/2} \sin 2\theta f\left(\sin \mathrm{\theta }+{\cos }^2\mathrm{\theta }\right)\mathrm{d\theta },\text{ then }$

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