A curve passes through $(1, 6)$, and its slope at every point $(x, y)$ is $2x + 3$. What is its equation?

Explanation

1. 01

   $y = \int (2x + 3)\,dx = x^{2} + 3x + C$.

2. 02

   Through $(1, 6)$: $6 = 1 + 3 + C$, so $C = 2$.