To calculate the surface area generated by curve `y=f(x)` revolving about `x`-axis between `a` and `b`, we use the following formula
`S_x=2pi int_a^b y sqrt(1+y'^2)dx`
Let us therefore first find the derivative `y'.`
We can now calculate the surface.
`2pi int_-1^1 2dx=4pi x|_-1^1=4pi(1+1)=8pi`
The area of surface generated by revolving the given curve about `x`-axis between `-1` and `1` is `8pi`.
Graphs of the curve and the surface generated by curve's revolution can be seen in the images below.