H = [a,b][tex]\times[/tex][c,d] . f[tex]\rightarrow[/tex]R is continuous, and 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.