Definite integrals via integration by parts

Find

1. \( \displaystyle \displaystyle \displaystyle\int_{0}^{1} xe^{x} \, \mathrm{d}x\)
2. \(\displaystyle \displaystyle \displaystyle\int_{0}^{\frac{\pi}{2}} x \cos x \, \mathrm{d}x\)