Question

Please help me with a Calc AB multiple choice. Happy holidays

Answer 1

By the fundamental theorem of calculus (FTC), we can say 
$\displaystyle \int_{a}^{b}f'(t)dt = f(b) - f(a)$
$\displaystyle \int_{0}^{4}f'(t)dt = f(4) - f(0)$

This means,
$\displaystyle \int_{0}^{4}f'(t)dt = 8$
$\displaystyle f(4) - f(0) = 8$
$\displaystyle f(4) - 5 = 8$
$\displaystyle f(4) - 5+5 = 8+5$
$\displaystyle f(4) = 13$

So that's why the answer is choice E) 13