Questions in definite-integral

Select	Question
	The value of $\int_{a}^{a+(\pi /2)}{({{\sin }^{4}}x+{{\cos }^{4}}x)\,dx}$ is
	$\int_{0}^{\pi }{{{\sin }^{5}}\left( \frac{x}{2} \right)\,dx}$ equals
	If $\int_{{}}^{{}}{f(x)\,dx}=x{{e}^{-\log \|x\|}}+f(x),$ then $f(x)$ is
	$\int_{0}^{\pi /2}{{{\sin }^{4}}x{{\cos }^{6}}x\,dx}$ equals
	The value of $\int_{\,0}^{\,\pi /2}{{{\left( \sqrt{\sin \theta }\cos \theta \right)}^{3}}d\theta }$ is
	$\int_{\,0}^{\,\infty }{\,\log \left( x+\frac{1}{x} \right)\frac{dx}{1+{{x}^{2}}}}$ is equal to
	$\int_{\,0}^{\,\infty }{\frac{x\ln x\,dx}{{{(1+{{x}^{2}})}^{2}}}}$ is equal to
	If $f(t)=\int_{\,-t}^{\,t}{\frac{dx}{1+{{x}^{2}}},}$ then ${f}'(1)$ is
	If $F(x)=\int_{{{x}^{2}}}^{{{x}^{3}}}{\log t\,dt,\,\,(x>0),}$ then ${F}'(x)=$
	$\int_{\,-\pi /2}^{\,\pi /2}{{{\sin }^{4}}x{{\cos }^{6}}x\,dx=}$