Bounds On Surface Of Revolution Integral? The question says:Set up …

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Bounds On Surface Of Revolution Integral? The question says:Set up an integral for the area of the surface obtained by rotating
the curve about y axis
Function: y=e^(-x^2) where x is equal to or between -1 and 1

What I did: integral(2pixds)
integral from -1 to 1 (2 * pi * x * square root ( 1 +4x^2 e^(-2x^2)

I got it wrong. The answer in the book says the bounds are 0 to 1. Everything else I did right.

Please tell me what i did wrong. I have a quiz tomorrow
so do you always do this when the bounds would be from a negative to positive? will the problems be “rigged” so that there is always symmetry when the bounds would be from a negative to positive?
sorry guys i’m still confused. is the back of the book wrong? there’s no other two’s in the answer key- it’s exactly the same thing i got except for the bounds.
ok i get kb and mathmom’s explanation i think

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