Consider the function defined implicitly by the equation `y^3-3y+x=0` on various intervals in the real line. If `x in (-oo,-2) uu (2,oo)`, the equation implicitly defines a unique real-valued defferentiable function `y=f(x)`. If `x in (-2,2)`, the equation implicitly defines a unique real-valud diferentiable function `y-g(x)` satisfying `g_(0)=0`.
The area of the region bounded by the curve `y=f(x)`, the X-axis and the line `x=a` and `x=b`, where `-oo lt a lt b lt -2` is

Options

A. `int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx+by(b)-af(a)`
B. `-int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx-by(b)+af(a)`
C. `int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx-by(b)+af(a)`
D. `-int_(a)^(b)(x)/(3[{f(x)}^(2)-1])dx+by(b)=af(a)`

Answer

A