integrals of composition of functions

Question

If $f$ and $g$ are measurable and integrable functions that are equal almost everywhere on a measurable space E, and $\int_E fdx = \int_E gdx $, does it hold that $\int_E sin (f(x)) dx = \int_E sin(g(x))dx $?

Answer 1

If $f=g$ almost everywhere on $E$ the $\int_E f =\int_Eg$ and $\int_E \sin f=\int_E \sin g$.

Integrability of $f$ and $g$ implies integrability of $\sin f$ and $\sin g$ becasue $|sin x | \leq |x|$.