How is it possible that is non periodic such as the Rect(x) function can be represented by a infinite sum of cosins and sins. I do not understand how this is visually possible.
Specifically how can the function have the value 0 going out to infinite if it is generated from sins and cosines.
NOTE: I am an electrical engineer who has a pretty good idea of how a Fourier series works and how complex numbers work but I just cant understand how a bunch of sins and cosines moving up and down can represent a nonperiodic function.
Sums and integrals are quite different! "Sum" made me think you were talking about Fourier series, not the Fourier transform.
For Fourier transforms, the idea is that the sines and cosines don't have commensurate frequencies; generally the frequency will take every possible value, so e.g. the Fourier integral can consist of an integral of sines / cosines where the frequency gets arbitrarily small / the period gets arbitrarily large. You can check that this is true of the Fourier transform of the rectangular function: every possible frequency occurs in the integral.
With Fourier series we restrict our attention to sines and cosines which all have frequencies an integer multiple of a fundamental frequency which is what keeps the whole sum periodic; with the Fourier transform we throw that out the window. Already a sum like $\sin x + \sin \pi x$ consisting of two sinusoids with incommensurate frequencies isn't periodic.