Integrating 2(100+t) A friend and I were doing some math together when we had to integrate $2(100 + t)$.
I just multiplied it out and integrated $200 + 2t$, which should be $200t + t^2$.
He did u-substitution and got $(100 + t)^2$.
When I take the derivative of both of ours, I seem to get the same thing. But $(100 + t)^2 = 10000 + 200t + t^2$, which is not equal to just $200t + t^2$.
What is going on here?

The difference is just the constant of integration.  Both your solutions are correct, as is any one of the form C+200t+t^2 for any constant C.
