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The final value of the integral is $1$. This is obtained by evaluating the recognized sine series at the endpoints of the interval: $\sin(\pi/2) - \sin(0) = 1 - 0 = 1$.

Conditions: The integration interval is $[0,\pi/2]$.; The integrated series has been correctly identified as the Maclaurin series for $\sin x$.; The Fundamental Theorem of Calculus is applied to evaluate the definite integral.

The final value of the integral is $1$. This is obtained by evaluating the recognized sine series at the endpoints of the interval: $\sin(\pi/2) - \sin(0) = 1 - 0 = 1$.

Conditions: The integration interval is $[0,\pi/2]$.; The integrated series has been correctly identified as the Maclaurin series for $\sin x$.; The Fundamental Theorem of Calculus is applied to evaluate the definite integral.