∫x(x^2+1)^5 dx from 0 to 2

Part I know:

substitution is u=x^2+1, du=2x dx, x=0 u=1, x=2 u=5

Part from solutions manual:

(1/2) ∫ (x^2+1)^5 (2x dx)

(1/2) ∫ u^5 du from x=1 to 5

[u/12] from 1 to 5

(5^6-1^6)/12

15624/12

answer = 1302

Now my questions:

Where did the 1/2 in front of the integral come from?

Where did the u/12 come from?

Is there a trick to this that I am just not seeing? -- Calc 2 is kicking my butt so far.