Fourier Series Co-efficents

I am trying to program a GUI that will plot the Fourier series of an input signal that will input into the GUI by the user. For simplicity, I have chosen the rect function. I have to do this lab only using the Legendre polynomials as my basis vector when determining the Fourier Co-Efficents. I am no sure where to begin. The value of n for the Fourier series will be determined by the scroll bar which the user will shift. I would like to know how to create a basis vector using the Legendre polynomials and how to use an integral in matlab to compute the corresponding Fourier co-efficents?