what's the Fourier transform of this function?

Suppose I have a function f(u),

and define g(s)=int(f(u), u from -inf to s),

what is the Fourier transform of this function? I could see it may need some 
additional conditions, or generalized Fourier transforms, etc.

Any thoughts? 

Wowow wrote:
> Suppose I have a function f(u),
> 
> and define g(s)=int(f(u), u from -inf to s),
> 
> what is the Fourier transform of this function? I could see it may
> need some additional conditions, or generalized Fourier transforms,
> etc.
> 
> Any thoughts?
> 
> 

Note that f is the derivative of g. Try integration by
parts for the Fourier transform of g, to obtain g' = f
in the integrand.

That should get you a relationship between the Fourier
transform of g and that of f.

Dale