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\int e^{t}\mathrm{d}t
Evaluate the indefinite integral first.
e^{t}
Use \int e^{t}\mathrm{d}t=e^{t} from the table of common integrals to obtain the result.
e^{x}-e^{0}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
e^{x}-1
Qisqartirish.