Using definite integrals

Calculus Level 2

A function \(f(x)=x^5-4ax^4+a^2x^3+x^2-ax+1\) satisfies the following condition:\[\frac{d}{dx}\int^x_0 f(t)dt = \int^x_1 \frac{d}{dt} f(t)dt.\] Find the sum of all possible values of \(a\).

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