Type functions and limits of integration in the corresponding input boxes and click on the check boxes to visualize the corresponding integrals; try for instance a) [math]f\left(x\right)=x^2+1[/math] , b) [math]f\left(x\right)=-x^2-1[/math] and c) [math]f\left(x\right)=1-x^2[/math] in the interval from [math]x=-2[/math] to [math]x=2[/math].

Distinguish between [b][i]the absolute value of the definite integral of a function[/i][/b] and [b][i]the definite integral of the absulute value of a function[/i][/b], in which cases are the values of these two integrals equal?, which of the integrals will always calculate correctly the area enclosed by a curve and the [math]x[/math] axis?