A volume is described as follows:
1.  the base is the region bounded by $\displaystyle {y}={e}^{{{2.5}{x}}}$, $\displaystyle {y}={2.5}{x}^{{2}}+{0.7}$ and $\displaystyle {x}={1}$;
2.  every cross section perpendicular to the x-axis is a square.

Find the volume of this object.

volume =