Let f(x) = int(x)^(x+(pi)/(3))|sin thet...

Let `f(x) = int_(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])`

`f(x)` is stricity increasing in this interval

`f(x)` is differentiable in this interval

Range of `f(x)` is `[2-sqrt(3)-1]`

`f(x)` has a maxima at `x = pi/3`

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