a) Calcule $ \int_{0}^1 x\sin\left( \pi x^2\right) dx. $ b) Calcule $ \lim_{n\to\infty} \frac{1}{n}\sum_{k=0}^{n-1} k\int_{\frac{k}{n}}^{\frac{k+1}{n}} \sin\left(\pi x^2\right) dx. $