Answer
$0$
Work Step by Step
Our aim is to solve the integral $\int_{1}^{\sqrt {\pi+1} } x \cos (x^2-1) \ dx$
Now, $\int_{1}^{\sqrt {\pi+1} } x \cos (x^2-1) \ dx=\dfrac{1}{2} \times [\sin (x^2-1)]_{1}^{\sqrt {\pi+1} }$
or, $=\dfrac{1}{2} \times [\sin (\sqrt {\pi+1} )^2-1)-\sin ((1 )^2-1)]$
or, $=\dfrac{1}{2} \times [\sin (\pi)-\sin (0)]$
or, $=0$
