Integral properties **Hi, someone knows how make the procedure to reach, this, I dont undestand how integration limits are change ** 


By definition of definite integration, if there exists a function, $G(x)$, derivable on the interval $x\in[a,b]$ then:
$$\frac{\mathrm{d} G(x)}{\mathrm {d} x} = g(x) \implies \int_a^b g(x) \;\mathrm{d}x = G(b)-G(a)$$
So if we take the identity (since $G(\color{red}{b})-G(\color{red}{b})=0$):
$$G(\color{blue}{c}) - G(\color{green}{a}) = G(\color{blue}{c})-G(\color{red}{b})+G(\color{red}{b})-G(\color{green}{a})$$
By substitution:
$$\therefore \int_{\color{green}{a}}^{\color{blue}{c}} g(x)\;\mathrm{d}x  = \int_{\color{red}{b}}^{\color{blue}{c}} g(x)\;\mathrm{d}x + \int_{\color{green}{a}}^{\color{red}{b}} g(x)\;\mathrm{d}x $$
That's how the interval limits work.
