Uniform convergence with $\sin^n(x)$

Question

I have to determinate the uniform convergence (set of convergence) and calculate the sum of this series: $$ \sum_{n=1}^\infty \sin^nx \frac{(-1)^{n-1} + n^2}{n} $$ For the convergence, I applied the definition, but I do not know how to treat the $\sin^n(x)$. Can someone explain me how to do this exercise, please? Thank you!