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\int \frac{\sin(x)}{2}\mathrm{d}x
Evaluate the indefinite integral first.
\frac{\int \sin(x)\mathrm{d}x}{2}
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
-\frac{\cos(x)}{2}
Use \int \sin(x)\mathrm{d}x=-\cos(x) from the table of common integrals to obtain the result.
-\frac{1}{2}\cos(\pi )+\frac{1}{2}\cos(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.
1
Simplify.