The symmetry axis is x = 1.
The minimum value of f (x) is 1,
∫ let f(x)=a(x- 1)2+ 1, (a > 0).
∫f(0)= 3，
∴a=2，
∴f(x)=2(x- 1)2+ 1, that is, f (x) = 2x2-4x+3.
(2) It can be known from the condition that the symmetry axis x of f(x) passes through the interval (2a, a+ 1).
∴2a< 1