Problem

The tangent, represented by the graph of the function

y = f(x)

, at the point with abscissa

x = 1

form an angle of

\pi/6

, at the point

x = 2

form an angle of

\pi/3

and at the point

x = 3

form an angle of

\pi/4

. Then, find the value of,

\int_1^3 f'(x) f''(x) dx + \int_2^3 f''(x) dx.