Find the area of the regions above the curve y -ex e2x-1

Question

Question: Find the area of the regions

1. Between the line y = 1 and one arch of y = sin θ.

2. Between y = -x² + 5x - 4 and the x-axis, 0 ≤ x ≤ 3.

3. Between y = cos x + 7 and y = ln(x - 3), 5 ≤ x ≤ 7.

4. Above the curve y = -ex + e^2(x-1) and below the x-axis, for x ≥ 0.