I'm asked to evaluate an indefinate integral $\int P dx$ by substitution. This is the first question:
$$ P= \frac {x^5+1}{x^2+1} $$
and my answer is
$$(\ln(x^2+1))/2+x^4/4-x^2/2+\arctan(x)+C$$
The second question is "Hence, solve the initial problem $\frac {dy}{dx} = P$ for y, where y = 1 at x = 0".
--- What do we mean by "solving the initial problem for y"?
My guess is to find the constant C by putting y = 1 and x = 0 into the answer $(\ln(x^2+1))/2+x^4/4-x^2/2+\arctan(x)+C$.
May I know if I guess correctly? Thank you for answering.