JEE 2023 — Mathematics PYQ

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