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Pari/gp delivers:

? s = 0.1;

? intnum( x=3.9, 4.1, exp( -(x-4)^2/2/s^2 ) / sqrt(2*Pi*s^2) )                                                                
%2 = 0.6826894921370858971704650911

We can do the same in sage, i.e. call gp:

sage: gp( "intnum( x=3.9, 4.1, exp( -(x-4)^2/2/%s^2 ) / sqrt(2*Pi)/%s)" % ( 0.1, 0.1 ) )
0.6826894921370858971704650911

Or call the numerical integral from sage:

sage: integral_numerical( lambda x :    exp( -(x-4)^2/2/0.1^2 ) / sqrt(2*pi)/0.1, 3.9, 4.1 )
(0.6826894921370853, 7.579375928402468e-15)

which computes the approximative value 0.6826894921370853 with an error less than $7,6\cdot 10^{-15}$, as given in the second argument.