TeX source:

\mathrm{B}(\mathrm{x})=\operatorname{area} \text { of trapezoid }=(\text { base }) \cdot(\text { average height })=(\mathrm{x}) \cdot\left(\frac{1+(1+x)}{2}\right)=\mathrm{x}+\frac{x^{2}}{2}