Find maximum value of f(x)=∫(2t-t²+5) in[0,x]

The roots of this equation : x = 1 + root(6), 1- root(6)
d/dx ( df/dx) = 2 - 2x
It is negative for the first root x = 1 + root(6)
Hence the maximum value can be found out by putting x = 1 + root(6) in the integral. Integrate the integral and find it.