For \(a<b\), total area between \(y=\mathrm{f}(x)\) and the \(x\)-axis is

\(A=\int_a^b|\mathrm{f}(x)|\,\mathrm dx\)

\(A=\displaystyle\int_a^b \mathrm{f}(x)\,\mathrm{d}x\)

\(A=-\displaystyle\int_a^b \mathrm{f}(x)\,\mathrm{d}x=\left|\displaystyle\int_a^b \mathrm{f}(x)\,\mathrm{d}x\right|\)

Split where the function changes sign and add positive areas. A touching zero with no sign change needs no split.

Area Enclosed by the Curve and the \(x\)-axis