Solving the equations

$$\begin{array}{r} (y-2)^2=x-1 \text { and } x-2 y+4=0 \\ x=2(y-2) \end{array}$$

$$\begin{aligned} & \frac{x^2}{4}=x-1 \\ & x^2-4 x+4=0 \\ & (x-2)^2=0 \\ & x=2 \end{aligned}$$

Exclose area (w.r.t. y-axis) $$=\int_\limits0^3 x d y-\text { Area of } \Delta$$.

$$\begin{aligned} & =\int_\limits0^3\left((y-2)^2+1\right) d y-\frac{1}{2} \times 1 \times 2 \\ & =\int_\limits0^3\left(y^2-4 y+5\right) d y-1 \\ & =\left[\frac{y^3}{3}-2 y^2+5 y\right]_0^3-1 \\ & =9-18+15-1=5 \end{aligned}$$