If the Fourier transform shows the magnitude of the frequency, in a $\sin(x)$ graph there is exactly one frequency.
So then why is there some "area" to the two spikes? Why are they not exactly straight lines? Is this just because of the limitation in resolution of numerical method to solve them?
Technically speaking, there are two spikes, since $\sin \omega x = \frac 1 {2i} \left ( e^{i\omega x}-e^{-i \omega x}\right)$, and thus there 2 frequencies ($\omega$ and $-\omega$).
Also, technically, those spikes are really Dirac delta distributions.
Finally, if you think you're seeing some "area" instead of pure spikes, I'm guessing you are looking at a tool that discretized the $\sin$ and computed its Discrete Fourier Transform (so not the "integral" Fourier transform). That discretization has an effect of transforming the true delta into a finite spike with "some area" underneath.
Finally, if you reduce the discretization step of your $\sin$, then you'll start seeing the bump with an area look more and more like a spike. In the limit, this would become a true Dirac delta.