Integrating the Fourier series mathematical methods student solutions

[BlackVegetable]

Anyone that can explain this as simply as possible, I would simply take the integral of both sides but why do they define F(-1)=0 and then go on to change the limits of integration with the addition of F(-1) which they later calculate as equal to -1/2 (as I can work out from taking the integral of
-x-1 with those limits)

Not getting any of the process,

 

[tkhunny]

Did you find the indefinite integral of each piece? That might be a good place to start thinking about it.

 

[BlackVegetable]

oops miss calculation I can see now that the definite integral gives the correct value. But why did they define F(-1) as zero as opposed to F(0)=0 , could you do either?