If the curve dips below the x-axis, the integral gives a signed area. This means the integral adds the part above the x-axis as positive and subtracts the part below the x-axis as negative. So, the result of \int_a^b f(x)\,dx can be positive, negative, or zero, depending on how much of the curve is above or below the x-axis.
If the curve dips below the x-axis the integral gives a signed area This means the integral adds the part above the x-axis as positive and subtracts the part below the x-axis as negative So the result of \int_a^b f(x)\dx can be positive negative or zero depending on how much of the curve is above or below the x-axis