Central moment for a uniform distribution

Question

The probability density function of T is given by

$$f(t) = 1/2h \text{, for each } t\in(-h,h) $$
where $h > 0$. Derive an expression for the central moment

I used integration and got $\frac{(b-u)^r+1 - (a-u)^r+1}{2h(r+1)}$ is this correct?