Answer
See below for detailed work.
Work Step by Step
$$A=\int x^n\sin xdx$$
We set $u= x^n$ and $dv=\sin xdx$
That makes $du=nx^{n-1}dx$ and $v=-\cos x$
Applying integration by parts $\int udv=uv-\int vdu$, we have
$$A=x^n(-\cos x)-\int nx^{n-1}(-\cos x)dx$$ $$A=-x^n\cos x+n\int x^{n-1}\cos xdx$$
The reduction formula has been established.
