Question

Find the fourier series of the function:
f(x)= {(2) -π≤x<0
{(6) 0≤x<π

Answer 1

Notice that

f(x) = 2 + 4.s(x)

where s(x) is the square wave function. And the Fourier series of the square wave function is standard, you've probably had it already in your lectures ... or you can find it here, page 3/4 onwards:
http://www.stewartcalculus.com/data/CALCULUS%20Early%20Transcendentals/upfiles/FourierSeries5ET.pdf