1103124301

The picture shows graphs of two quadratic functions $f_1(x)$ and $f_2(x)$. Find the unknown real positive constant $a$ (as shown in the picture) such that the value of the definite integral $\underset{-1}{\overset{1}{\int }}{f}_1(x)\mathrm{d}x$ is greater by $8$ than the value of the definite integral $\underset{-1}{\overset{1}{\int }}{f}_2(x)\mathrm{d}x$.