Answer
$F(4)=24$
Work Step by Step
Suppose that $F$ is an antiderivative of $f$ so:
$$F'(x)=f(x)$$
Using the $FTC$ the following is true:
$$\int_{1}^{4}f(x)dx=F(4)-F(1)$$
$$\int_{1}^{4}F'(x)dx=F(4)-F(1)$$
$$\int_{1}^{4}x^{2}dx=F(4)-F(1)$$
$$[\frac{x^{3}}{3}]_{1}^{4}=F(4)-F(1)$$
$$\frac{4^{3}}{3}-\frac{1^{3}}{3}=F(4)-F(1)$$
$$21=F(4)-F(1)$$
$$21=F(4)-3$$
$$21+3=F(4)$$
$$24=F(4)$$
