How they do those transitions?

[nhrock3]

http://i46.tinypic.com/3145l77.jpg



by what laws they do the red and bue transitions

?

 

[rock.freak667]

From what I can deduce:

$$\int_a ^{b} F(x) dx = \int_c ^{b} F(x) dx + \int_a ^{c} F(x) dx$$


and then it looks like for the blue, the period is π such that f(x+π)=f(x)

 

[nhrock3]

how they go from x+pi to x
?

 

[Mark44]

I suspect that it has to do with how f(x) is defined at the top of your work.

BTW, the work you posted is extremely difficult to read. You're likely to get more help if people here can read what you have written. It would be better if you rewrote it without all the stuff you crossed out.