## gaussian integral

Hello,
I have the following equation, where f(x) is the function I am looking to find:

$\int _{ a }^{ b }{ { e }^{ -{ ((u-x)/s) }^{ 2 } }f(x) } dx\quad ={ e }^{ -{ ((u-c)/s) }^{ 2 } }\quad$

Where c = (b-a) / 2

I assume f(x) is also some guassian.. but can't find a solution for this.
any ideas?