Question

WILL BECOME A FAN AND GIVE A MEDAL
If f'(x)= 3x^2 and f(-1)=2, then integral from 0 to 2 of f(x) dx=
(A) 8/3
(B) 4
(C) 7
(D) 10
(E) 28

Could you please show your work as well as select an answer? I'd really appreciate it!

Answer 1

f'(x)=3x^2
f(x)=integral 3x^2dx=3x^3 /3 +c=x^3+c
f(-1)=(-1)^3+c
2=-1+c
c=3
f(x)=x^3 +3
again f'(x)=3x^2
f(x)=integral 0 to 2 3x^2 dx=[3x^3 /3 ] ,0 to2 =[x^3],0 to2 =[(2)^3-0^3]=8