u substitution

${\int }_{-1}^{4}x(x^2-3{)}^{5}dx$
${\int }_{-1}^{4}x{u}^{5}dx$

$u=x^2-3$
$\frac{d}{dx}[u]=\frac{d}{dx}[x^2-3]$
$\frac{du}{dx}=2x$
$du=2xdx$

$u=-1^2-3$
$u=-2$

$u=4^2-3$
$u=13$

$\frac{1}{2}{\int }_{-2}^{13}2x{u}^{5}dx$
$\frac{1}{2}{\int }_{-2}^{13}{u}^{5}du$