Please Help!!

I am struggling with this since hours!

How is it possible then, that for example if c = 0.1, a = 1.0 / (0.1 * sqrt(2.0 * PI)) = 3.9894228.the gaussian function is $\displaystyle g(x) = a*exp(-(x-b)^2/(2*c^2))$

This integral is 1 if and only if $\displaystyle a = 1/(c*sqrt(2*PI))$.

I mean how can the integral be one, if g(0) is larger than one??

Any ideas what my mistake is here?

Thanks a lot!!!