# Why can Fourier series be used on a non-repetitive function?

I was just wondering why Fourier series can be used on the function in the linked image. This is since I thought the function had to repeat itself to use Fourier series on it. Or is it saying a period is from 0-5s and so it will repeat every 0-5s? like the 2nd graph i made?

I can find the answer easily just not sure why fourier series can be used?

Fourier series can be calculated for any signal in close section (from $T_0$ to $T_1$). In fact, I was taught that this is how Fourier series is defined.
But Fourier series is made up of ($T_0 - T_1$) cyclic functions, therefore, if you go beyond the original section you will just get repetitions as you displayed.