By the fundamental theorem of calculus (FTC), we can say
[tex]\displaystyle \int_{a}^{b}f'(t)dt = f(b) - f(a)[/tex]
[tex]\displaystyle \int_{0}^{4}f'(t)dt = f(4) - f(0)[/tex]
This means,
[tex]\displaystyle \int_{0}^{4}f'(t)dt = 8[/tex]
[tex]\displaystyle f(4) - f(0) = 8[/tex]
[tex]\displaystyle f(4) - 5 = 8[/tex]
[tex]\displaystyle f(4) - 5+5 = 8+5[/tex]
[tex]\displaystyle f(4) = 13[/tex]
So that's why the answer is choice E) 13
