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Let I be the rectangle [0, 5] × [0, 5] in the plane R². Define the function f: I→ R by f(x, y) = Y, 0043 X, y > x, y ≤ x. For k ≥ 3, let P be the regular partition of [0, 5] into k partition intervals, and let Pk = (Pk, Pk) be the corresponding partition of I. (a) Evaluate U(f, Pk) and L(f, Pk) for each k ≥ 3. (b) Find the limits lim U(f, Pk) and lim L(f, Pk). k→∞ (c) Use your result in part (b) to conclude that f: I→ R is integrable and find 1₁