Given the probability density function $f(x)=e^x$ and a mean of 16, find $P(X<20)$.

I did: $$P(X<20)=\int_{-\infty}^{20}e^{x}dx=e^{x}\bigg\rvert_{-\infty}^{20}\big[e^{20}-e^{-\infty}\big]=e^{20}$$

But a probability has to be between 0 and 1. I would appreciate some help, thanks.