Question

Suppose that f is a continuous real-valued function defined on the unit square in
IR2: {(x, y) : 0 ≤ x, y ≤ 1}.
Let F(x) = integral from 0 to 1 f(x,y) dy, 0 ≤ x ≤ 1.
Prove that F is continuous.

This is for Real Analysis 2

Answer 1

*that is \[Let F(x) =\int\limits_{0}^{1} f(x,y) dy, 0 ≤ x ≤ 1\]