Answer
$f(x)=x^{5}-x^{3}+4x+6$
Work Step by Step
Find the antiderivative
$f'(x)=5x^{4}-3x^{2}+4$
$f(x)=\int5x^{4}-3x^{2}+4dx$
$f(x)=\frac{5x^{4+1}}{4+1}-\frac{3x^{2+1}}{2+1}+4x+C$
$f(x)=\frac{5x^{5}}{5}-\frac{3x^{3}}{3}+4x+C$
Simplify:
$f(x)=x^{5}-x^{3}+4x+C$
Find the value of C given $f(-1)=2$
$f(x)=(-1)^{5}-(-1)^{3}+4(-1)+C=2$
$f(x)=-1+1-4+C=2$
$f(x)=-4+C=2$
$C=6$
