Let f:[-3,1] → R be given as f(x)= {min {(x+6), x^2}, -3 ≤ x ≤ 0; max {√ x, x^2}, 0 ≤ x ≤ 1.} If the area bounded by y=f(x) and x -axis is A, then…

Let $\displaystyle f:[-3,1] \rightarrow \mathbf{R}$ be given as $$f(x)=\left\{\begin{array}{lr} \min \left\{(x+6), x^2\right\}, & -3 \leq x \leq 0 \\ \max \left\{\sqrt{x}, x^2\right\}, & 0 \leq x \leq 1 . \end{array}\right. $$ If the area bounded by $\displaystyle y=f(x)$ and $\displaystyle x$-axis is A , then the value of $\displaystyle 6$ A is equal to \_\_\_\_.