Using integration, find the area of triangle $\mathrm{ABC}$, whose vertices are $\mathrm{A}\left(2,5\right),\mathrm{B}\left(4,7\right)$ and $\mathrm{C}\left(6,2\right)$.
OR
Find the area of the region lying above $\mathit{x}$-axis and included between the circle ${\mathit{x}}^2+{\mathit{y}}^2=8\mathit{x}$ and inside of the parabola ${\mathit{y}}^2=4\mathit{x}$.