The equation of a curve is given by $y=f\left(x\right)$ where
$f^{\mathrm{\prime }}\left(x\right)$ is a continuous function. The tangent at points

$(1, f(1\left)\right) , (2,f(2\left)\right)$ and $(3,f(3\left)\right)$ make angles $\frac{\pi }{6},\frac{\pi }{3}$

and $\frac{\pi }{4}$ respectively with positive x-axis. Then

${\int }_2^3 f^{\mathrm{\prime }}\left(x\right)f^{\prime \prime }\left(x\right)\mathrm{d}x+{\int }_1^3 f^{\prime \prime }\left(x\right)\mathrm{d}x$ is

• A

  1

• B

  $-\frac{1}{\sqrt{3}}$

• C

  $\frac{1}{\sqrt{3}}$

• D

  0