Let $f(x)={\int }_{0}^{x}t\left({t}^{2}-3t+20\right)dt,x\in (1,3)$ and range of f(x) is $(\alpha ,\beta )$, then $\alpha +\beta$ is equal to

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Let \(f(x)={\int }_{0}^{x}t\left({t}^{2}-3t+20\right)dt,x\in (1,3)\) and range of f(x) is \((\alpha ,\beta )\), then \(\…