$\frac{d}{d x} \int_{a}^{b} \sin x^{r} d x$
Final Answer: \(\boxed{r x^{r-1} \cos(x^r)}\)
Step 1 :Find the derivative of the integral of sin(x^r) with respect to x using the Fundamental Theorem of Calculus: f(x) = sin(x^r)
Step 2 :Calculate the derivative: \(r x^{r-1} \cos(x^r)\)
Step 3 :Final Answer: \(\boxed{r x^{r-1} \cos(x^r)}\)