`int_(-pi/6)^(pi/6)sin^5xdx`

Explanation

Let `f(x)=sin^5x`
Then`f(-x)=sin^5(-x)`
=`-sin^5x=-f(x)`
So f(x) is an odd function.
Thus `int_-a^af(x)dx=0`
`therefore int_(-pi/6)^(pi/6) sin^5xdx=0`