Using substitution for definite integral

Question

I chose E for this question, but the answer is C. Why does the interval changes after the substitution?

I first calculate $du = 2x \space dx$ and then substitute $u$ and $du$ into the expression and get the answer is E, what am I doing wrong?

Answer 1

You have to change the bounds of the integral according to the $u$-substitution.

When $x$ goes from $-1$ to $4$, and $u=x^2-3$, you have $u$ goes from $(-1)^2-3=-2$ to $4^2-3 = 13$.

Answer 2

We let $u=x^2-3$, that is we want to expressed everything in $u$.

When $x=-1$, the corresponding $u$ is $(-1)^2-3=-2$.

When $x=4$, the corresponding $u$ is $(4)^2-3=13.$