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Total number of distinct `x epsilon [0,1]` for which `int_(0)^(x) (t^(8)+1)/(t^(8)+t^(2)+1) dt=3x-2` is ______

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The correct Answer is:
1
Let `f(x)=int_(0)^(x) (t^(8)+1)/(t^(8)+t^(2)+1)dt-3x+2`
`f(0)=2, f(1)=` negative
So, `f(x)` has one root in`[0,1]`
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