Chapter 5.4, Problem 70E

HOW DO YOU SEE IT? The graph of f is shown in the figure. The shaded region A has an area of 1.5, and ${\displaystyle {\int }_0^{6}f\left(x\right)dx=3.5}$. Use this information to fill in the blanks.

(a). ${\displaystyle {\int }_0^{2}f\left(x\right)dx=\boxed{}}$

(b). ${\displaystyle {\int }_2^{6}f\left(x\right)dx=\boxed{}}$

(c). ${\displaystyle {\int }_0^6\left|f\left(x\right)\right|dx=\boxed{}}$

(d). ${\displaystyle {\int }_0^2-2f\left(x\right)dx=\boxed{}}$

(e). ${\displaystyle {\int }_0^6\left[2+f\left(x\right)\right]dx=\boxed{}}$

(f). The average value of f over the interval [0, 6] is $\boxed{}$