Integration of shifted Gaussian Distribution function giving incorrect answer

When I integrate the standard distribution function with shifting factor mu = 0 and sigma = .01, I get the expected result of 1:

p1 = @(x) gaussian_const .* exp(-((x)./(2.*sigma)).^2);
int = integral(p1,-Inf,Inf)

but if I make mu a large enough number or shift the function right or left, the integration returns a very small number. For example mu = 5,

p1 = @(x) gaussian_const .* exp(-((x-5)./(2.*sigma)).^2);
int = integral(p1,-Inf,Inf)

returns a near-zero value. Smaller values of mu, for example 1 or 2, still give the correct value of 1; but once I try 3 it returns very small number again.

Larger sigma values also seem to increase the range for what mu can be before I get zeros as answers. Any thoughts on why this is happening? I'm using this function to approximate the Dirac delta function, so very small sigma values are important.