Use the formula

to find the solution to the heat equation on the real line with initial condition .

My biggest, and maybe only, problem is trying to figure out what to 'do' with the f(y) in the integral, what does it represent?!? As i was typing this though something to do with popped into my head however im not sure if this applies to this situation or where i have seen/used it...

Anyone able to give me nudge in the right direction?