Find the equation of the line that passes trough point (0,1) such that the area, S, of the region enclosed by this line and the parabola y=x^2 is (5√5)/6.

This is what I did:

I found the equation of the line which is y=x+1

Then, I put x^2=x+1

x^2-x-1=0

α+β=-1

αβ=-1

S=integral of (x+1-x^2)dx [α,β].

It gave me (5√5)/6.

I don't know how to continue to find out the equation.

Please help me!