Let the area enclosed by the lines x+y=2, y =0, x=0 and the curve f(x)= min {x^2+3/4, 1+[x]} where [x] denotes the greatest integer ≤ x, be A. Then…

Let the area enclosed by the lines $\displaystyle x+y=2, \mathrm{y}=0, x=0$ and the curve $\displaystyle f(x)=\min \left\{x^2+\frac{3}{4}, 1+[x]\right\}$ where $\displaystyle [x]$ denotes the greatest integer $\displaystyle \leq x$, be A . Then the value of $\displaystyle 12$ A is $\displaystyle \_\_\_\_$