Free particle solution of the Schrodinger eq. in integral form?

Hi everyone! Sorry about formatting, I have no idea how to do it right :p I'll use f(x, t) for wave function and h instead of h-bar

So I have the free particle Schrodinger equation

d(f(x, t))/dt = ih/2m d²(f(x, t))/dx²

And have to find the general solution but in integral form! And I have no idea how to do it, I'm supposed to find that

f(x, t) = (integral from minus infinity to infinity) dk g(k) exp(ikx) exp(-ihk²t/2m)

But... I have no idea how to get there.