Can you tell me why

1. To find the area under a curve bounded by 2 x-values, I integrated the curve and substituted the x-values. The area came out -ve.
2. To find the area under a curve bounded by 2 x-values, I integrated the curve and substituted the x-values. The area came out zero, 0.
3. Why is the integral of e^-x = -e^-x and not e^-x?
4. Why is the integral of e^9x = 9e^9x and not e^9x?
5. How can this be solved for x 3 x^2 - 12 = 0?
6. How can this be solved for x 3/2 x^2 - 12/x = 0?