Q about an activation function

Does somebody know what is the 'exact' value if one
integrates h := x -> exp(-1/(1-x^2)) from -1 to +1
(or from 0 to 1)? I mean in terms of known constants,
not the numerical value.

Or for g := x -> exp(-1/x)/(exp(-1/x)+exp(-1/(x-1)))
integrated from 0 to 1?
.