Not complex at all

Calculus Level 5

If

01(3)xdx=a+ib\large{\displaystyle{\int _{ 0 }^{ 1 }{ { (-3) }^{ x } } dx=-a+ib}}

where ii is imaginary unit. Find 100ab\left\lfloor 100ab \right\rfloor .

Note: That the principal value of the complex exponentiation.

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