Not complex at all

Calculus Level 5

If

\[\large{\displaystyle{\int _{ 0 }^{ 1 }{ { (-3) }^{ x } } dx=-a+ib}}\]

where \(i \) is imaginary unit. Find \(\left\lfloor 100ab \right\rfloor \).

Note: That the principal value of the complex exponentiation.

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