$F\left( x \right)=\int{f\left( x \right)}$
$F\left( x \right)=\int{\sin x+\cos x}$
$F\left( x \right)=-\cos x+\sin x+C$
$\,\,\,\,\,\,\,F\left( \dfrac{\pi }{2} \right)=2$
$\Leftrightarrow -\cos \dfrac{\pi }{2}+\sin \dfrac{\pi }{2}+C=2$
$\Leftrightarrow C=1$
Vậy $F\left( x \right)=-\cos x+\sin x+1$