Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$

Question

$\begin{array}{1 1}8+\large\frac{e^8-1}{2} \\7+\large\frac{e^8+1}{2} \\6+\large\frac{e^8}{2} \\5+\large\frac{e^8-3}{2}\end{array}$