When is the dirac delta function taken as 1 and when it is taken as infinity I understand that the dirac delta function basically describes a pulse of area one, if the pulse is very narrow, the height will be infinity. However, Im confused because sometimes, people consider the dirac delta function as being one at t=0 (AKA the unit impulse function) rather than infinity, so when is it considered to be one rather than infinity? 
P.S. In MATLAB the dirac delta function is infinity at t=0

As you say, the "value" of the delta "function" is infinite at $0$ and the "area under it" is $1$.  I am not aware of any time we take the value to be $1$.  The unit impulse refers to the total impulse delivered, which is the area under the force-time curve.  
