The area included between y^2=4x, y=x+1 and x-axis is :

$y^2=4x, y=x+1$

finding intersection point

$(x+1)^2=4x$

$x^2+2x+1=4x$

$x^2-2x+1=0$

$(x-1)^2=0$

$x=1$

so $y=2$

area = 0

as curves are non intersecting