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g:[a,b][tex]\rightarrow[/tex]R is integrable.

Prove that

F(y) = [tex]\int[/tex]g(x)f(x,y)dx from a to b is uniformly continuous.

I initially ripped g(x) and f(x,y) apart and tried to show each was continuous. This failed.

In short, I am completely stuck. Please help me.