Questions in definite-integral

Select	Question
	$\int_{0}^{\infty }{{{e}^{-2x}}(\sin 2x+\cos 2x)\,dx=}$
	$\int_{0}^{b-c}{\,\,{f}''(x+a)\,dx=}$
	The greatest value of the function $F(x)=\int_{1}^{x}{\,\,\|t\|\,dt}$ on the interval $\left[ -\frac{1}{2},\,\,\frac{1}{2} \right]$ is given by
	$\int_{-\pi /2}^{\pi /2}{{{\sin }^{2}}x{{\cos }^{2}}x(\sin x+\cos x)\,dx=}$
	$\int_{0}^{\infty }{\frac{dx}{{{\left( x+\sqrt{{{x}^{2}}+1} \right)}^{3}}}}=$
	The derivative of $F(x)=\int_{{{x}^{2}}}^{{{x}^{3}}}{\frac{1}{\log t}\,dt}$, $(x>0)$ is
	If $f(x)=\int_{{{x}^{2}}}^{{{x}^{2}}+1}{{{e}^{-{{t}^{2}}}}}dt,$ then $f(x)$ increases in
	If $f(x)=\int_{{{x}^{2}}}^{{{x}^{4}}}{\sin \sqrt{t}\,dt,}$ then ${f}'(x)$ equals
	If $F(x)=\frac{1}{{{x}^{2}}}\int_{4}^{x}{(4{{t}^{2}}-2{F}'(t))\,dt,}$ then ${F}'(4)$ equals
	The value of the integral $\sum\limits_{k=1}^{n}{\int_{0}^{1}{f(k-1+x)\,dx}}$ is