The tangent of the curve \[y=f(x)\] at the point with abscissa \[x=1\] from an angle of \[\pi /6\] and at the point \[x=2\] an angle of \[\pi /3\] and at the point \[x=3\] an angle of \[\pi /4\]. If \[f''(x)\] is continuous, then the value of \[\int\limits_{1}^{3}{f''(x)f'(x)dx+\int\limits_{2}^{3}{f''(x)dx}}\] is

• A. \[\frac{4\sqrt{3}-1}{3\sqrt{3}}\]
• B. \[\frac{3\sqrt{3}-1}{2}\]
• C. \[\frac{4-3\sqrt{3}}{3}\]
• D. None of these