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Differentiate w.r.t. y
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\int e^{y}\sin(z)\mathrm{d}x
Evaluate the indefinite integral first.
e^{y}\sin(z)x
Find the integral of e^{y}\sin(z) using the table of common integrals rule \int a\mathrm{d}x=ax.
e^{y}\sin(z)e-e^{y}\sin(z)
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.
\sin(z)\left(e-1\right)e^{y}
Simplify.