AreaAbove=If(I_{fac}≥0 ∧ I_{fcd}<0 ∧ I_{fdb}<0,I_{ac},I_{fac}<0 ∧ I_{fcd}≥0 ∧ I_{fdb}<0,I_{cd},I_{fac}<0 ∧ I_{fcd}<0 ∧ I_{fdb}≥0,I_{db},I_{fac}≥0 ∧ I_{fcd}≥0 ∧ I_{fdb}<0,I_{ad},I_{fac}≥0 ∧ I_{fcd}<0 ∧ I_{fdb}≥0,I_{ac}||I{db},I_{fac}<0 ∧ I_{fcd}≥0 ∧ I_{fdb}≥0,I_{cb},I_{fac}≥0 ∧ I_{fcd}≥0 ∧ I_{fdb}≥0,I_{ad}) AreaBelow=If(I_{fac}<0 ∧ I_{fcd}≥0 ∧ I_{fdb}≥0,I_{ac},I_{fac}≥0 ∧ I_{fcd}<0 ∧ I_{fdb}≥0,I_{cd},I_{fac}≥0 ∧ I_{fcd}≥0 ∧ I_{fdb}<0,I_{db},I_{fac}<0 ∧ I_{fcd}<0 ∧ I_{fdb}≥0,I_{ad},I_{fac}<0 ∧ I_{fcd}≥0 ∧ I_{fdb}<0,I_{acdb},I_{fac}≥0 ∧ I_{fcd}<0 ∧ I_{fdb}<0,I_{cb},I_{fac}<0 ∧ I_{fcd}<0 ∧ I_{fdb}<0,I_{ad}) Absolute Integral \begin{align}\color{0,0,255}\textsf{Area of the region above x-Axis}&\color{0,0,255}=\mathsf{}\\\color{127,0,255}\textsf{Area of the region below x-Axis}&\color{127,0,255}=\mathsf{}\\\color{0,0,255}\textsf{Total Area}&\color{0,0,255}=\mathsf{}\\\\\\\color{0,51,153}\textsf{\begin{pmatrix}Area bounded by the curve f,\\x-Axis and the ordinates\\x = and x = \end{pmatrix}}&\color{0,51,153}\mathsf{=\int\limits_{a}^{c}{\begin{vmatrix}f(x)\end{vmatrix}~dx}+\int\limits_{c}^{d}{\begin{vmatrix}f(x)\end{vmatrix}~dx}+\int\limits_{d}^{b}{\begin{vmatrix}f(x)\end{vmatrix}~dx}}\\&\color{0,51,153}\mathsf{=\int\limits_{}^{}{\begin{vmatrix}\end{vmatrix}~dx}+\int\limits_{}^{}{\begin{vmatrix}\end{vmatrix}~dx}+\int\limits_{}^{}{\begin{vmatrix}\end{vmatrix}~dx}}\\&\color{0,51,153}\mathsf{=\left[\right]_{}^{}\\~~~~+\left[\right]_{}^{}\\~~~~+\left[\right]_{}^{}}\\&\color{0,51,153}\mathsf{=++}\\&\color{0,51,153}\mathsf{=}\textsf{ sq. units}\end{align} if(a0&&b>0))&&(c < a ∨ c > b)&&(d < a ∨ d > b), abs(I_{ab}),(a<0&&b>0)∨(a>0&&b<0)&&(c < a ∨ c > b)&&(d < a ∨ d > b),abs(I_{0a})+abs(I_{0b}),0 b) ∧ (d < a ∨ d > b), abs(I_{0a}) + abs(I_{0b})) I=if(a<=b<=0<=c<=d∨a<=b<=0<=d<=c∨a<=b<=c<=0<=d∨a<=b<=d<=0<=c∨a<=b<=c<=d<=0∨a<=b<=d<=c<=0∨0<=a<=b<=c<=d∨0<=a<=b<=d<=c∨c<=a<=b<=0