Constant when integrating I was integrating $(t+2)^2$ by using the substitution method and by expanding the function. By expanding it then integrating I got the same answer as the book ($\frac{1}{3}(t^3+6t^2+12t)+C$), but when I substituted I got $\frac{1}{3}\cdot(t+2)^3 + C = \frac{1}{3} \cdot (t^3+6t^2+12t+8) + C$.
Am I missing something here? Got an 8 at the end when substituting, but no constant when expanding.

Your answers differ by a constant factor, so the values of $C$ will be different in these 2 methods.
In other words,
$$
\frac{t^3+6t^2+12t}{3} + C= \frac{t^3 + 6t^2 + 12t +8}{3} + K
$$
just $C = K + 8/3$...
