$f\left(x\right)$ is a continuous and bijective function on $R\dot{}$ If $\forall t\in R,$ then the area bounded by $y=f\left(x\right),x=a-t,x=a,$ and the x-axis is equal to the area bounded by $y=f\left(x\right),x=a+t,x=a,$ and the x-axis. Then prove that ${\int }_{-\lambda }^{\lambda }{f}^{-1}\left(x\right)dx=2a\lambda \left(giventhatf\left(a\right)=0\right)\dot{}$

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