Answer
$\dfrac{9}{2}$
Work Step by Step
Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$
Thus, the area of the region is:
$A=\int_a^b [f(x)-g(x)] \ dx= \int_{2}^{5} [(5x-9)-(x-1)^2] \ dx \\=\int_2^5 [5x-9-(x^2-2x+1)] \ dx \\=\int_2^5 (-x^2+7x-10)\ dx \\=[-\dfrac{x^3}{3}+\dfrac{7x^2}{2}-10x]_2^5 \\=\dfrac{-125}{3}+\dfrac{175}{2}-50+\dfrac{8}{3}-14+20 \\=\dfrac{9}{2}$
