Answer
$f(x) =2x^{2}+x^{3}+2x^{4}+2x+3$
Work Step by Step
$f''(t)==4+6x+24x^{2}$
Using the antiderivatives table,
$f'(t)=4x+3x^{2}+8x^{3}+C$
Using the antiderivatives table,
$f(x) =2x^{2}+x^{3}+2x^{4}+Cx+D$
$\left\{\begin{array}{llll}
f(0)=3 & \Rightarrow & D=3 & \\
f(1)=10 & \Rightarrow & & 2+1+2+C+3=10\\
& & & C=2
\end{array}\right\}$
$f(x) =2x^{2}+x^{3}+2x^{4}+2x+3$
