$\text{ Assertion (A): }{\int }_{\frac{\mathrm{\pi }}{6}}^{\frac{\mathrm{\pi }}{3}} \frac{(\sin \mathrm{x}{)}^{\sqrt{2}}\mathrm{dx}}{(\sin \mathrm{x}{)}^{\sqrt{2}}+(\cos \mathrm{x}{)}^{\sqrt{2}}}=\frac{\mathrm{\pi }}{12}$

$\text{ Reason }\left(\mathbf{R}\right):{\int }_{\frac{\mathrm{\pi }}{6}}^{\frac{\mathrm{\pi }}{3}} \frac{\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}}{\mathrm{f}\left(\frac{\mathrm{\pi }}{2}-\mathrm{x}\right)}=\frac{\mathrm{\pi }}{12}$

A is true. R is true and R is the correct explanation of A 

A is true, R is false

A is false, R is true 

A is true, R is true but R is not the correct explanation of A