Prove the surface integral of a constant vector field over a surface is equal to the area of the surface times the norm of vector field

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I have a question as below.

Prove that the surface integral of a constant vector field $F$ over a surface $S$ is equal to the area of $S$ times the norm of $F$, or find counter example.

I think it is true because my textbook gives equation as $$\int\int_S F \cdot n\ dA$$ where $n$ is the normal vector. I think this is exactly what the question states but how do I prove it?? Or am I wrong??

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