Unfortunately, this is not yet built in to Mathematica. It should be.
You can calculate
In[7]:= (1/(2 Pi)) Integrate[Exp[I k (x - x0)], {k, -a, a}]
Out[7]= Sin[a (x - x0)]/([Pi] (x - x0))
The limit as a->Infinity is a well-known representation of the delta function.
