Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 278: 4

\[ \begin{array}{c} 1+2 x=f(x) \\ x+3+x^{2} =G(x) \end{array} \]

\[ \begin{array}{c} 1+2 x =\frac{d y}{d x}=f(x) \\ C+x+x^{2}=G(x) \end{array} \] Substitute $x=1, G=5,$ and solve for $C$ \[ 1+1+C=5 \] \[ C=3 \] And therefore \[ x+3+x^{2}=G(x) \]