[tex]\displaystyle f(x) = 2x-3,\quad g(x) = x-1\\ \\ \diamond\,Gf \cap Gg:\,\,2x-3 = x-1 \Rightarrow x = 2\\ \\ A = \int_{0}^{2}\big[(x-1) - (2x-3)\big]\, dx \\ \\ =\int_{0}^{2}(-x+2)\, dx\\ \\ =-\int_{0}^2(-x+2)'\cdot (-x+2)\, dx\\ \\ = -\dfrac{(2-x)^2}{2}\Big|_{0}^2\\ \\ = -\dfrac{(2-2)^2}{2}+\dfrac{(2-0)^2}{2}\\ \\ = 0+\dfrac{4}{2}\\ \\ = \boxed{2}[/tex]
