Why can’t Mathematica integrate Poisson distribution?

 Why cant Mathematica integrate Poisson distribution?

Whenever I try to integrate the Poisson distribution

$ $ P(\lambda,x) = e^{-\lambda}\frac{\lambda^x}{x!} =e^{-\lambda}\frac{\lambda^x}{\Gamma(x+1)} $ $

 Integrate[Exp[-\[Lambda]] \[Lambda]^x/x!, {x, 0, Infinity}, Assumptions -> {\[Lambda] > 0}] 

Mathematica cannot do it. It returns the exact thing you input.

But this integral, as a probability distribution function, should integrate to 1 and be within the program’s capabilities, shouldn’t it?

It could be that I’m unaware of something about $ P(\lambda,x)$ as I’m currently learning this stuff.

Edit: I’ve learned the integral is not equal to 1. Regardless, why can’t Mathematica handle this?

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