# Evaluate the definite integral $\displaystyle\int\limits_0^1(xe^x+\sin\frac{\pi\;x}{4})dx$
$\begin{array}{1 1} 1+\large \frac{4}{\pi}-\frac{2 \sqrt 2}{\pi} \\1-\large \frac{4}{\pi}+\frac{2 \sqrt 2}{\pi} \\ 1-\large \frac{2}{\pi}+\frac{4 \sqrt 2}{\pi} \\ 1-\large \frac{2}{\pi}-\frac{2 \sqrt 4}{\pi} \end{array}$