## Calculus, 10th Edition (Anton)

$$f(x)= \frac{1}{3}(x+1)^3+ \frac{25}{3}$$
Given: Slope$=(x+1)^2$ and passes through $(-2,8)$ Since the curve is given by \begin{align*} f(x)&=\int (x+1)^2dx\\ &=\frac{1}{3}(x+1)^3+c \end{align*} Since the curve passes through $(-2,8)$, then $c=25/3$ and $$f(x)= \frac{1}{3}(x+1)^3+ \frac{25}{3}$$