Integral of upper incomplete gamma function

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Can anyone please help me with the integral below. I would like to know whether the following relation is correct?

$\int\big(\frac{t}{A}\big)^{n-1}\exp\big(-\frac{t}{A}\big) dt = -A\Gamma(n, \frac{t}{A})$

where $\Gamma(n, \frac{t}{A})$ is the upper incomplete gamma.

Best,