White Noise
The PSD is an even function, thus Sn(-w) = Sn(w).
For the white noise the PSD is a constant "C" in practical values of frequency. For instance we can call "C" of N/2 , thus we can say that the PSD of the white noise is constant with the value of N/2.
The power over a range of frequency is the integral of the PSD in the specified range. As the PSD of white noise is constant we can say that P = (N/2)* 2* (Delta F), where delta F is the range of frequency ( positive values) . The question raised here is why multiplying by 2 ? The answer is simple for each positive interval of frequency we have a correspondent negative interval of frequency so that we need to consider both areas in the integration: areas due to positive and negative frequency intervals.
Now imagine if you have the frequency interval from 0 to wo , we have P = (N/2)*2*( wo-0) = N*wo, now consider wo goint to infinite. It is just your question... the positive range of frequency . Thus P = N*(positive range of frequency), now can you realize the answer of you question? I hope so.
By the way, there is nothing to do with what you can see in a spectrum analyzer. Negative frequency is a mathematical tool very useful in solving problems in real world.