Let y=f(x) be a thrice differentiable function in (−5,5). Let the tangents to the curve y=f(x) at (1,f(1)) and (3,f(3)) make angles 6π and 4π, respectively, with the positive x-axis. If 2∫311((f′(t))2+1)f′′(t)dt=α+β3 where α, β are integers, then the value of α+β equals