see the attached figure to better understand the problem
step 1
Find out the area of the function y=-1 , in the interval [-1,0]
A=(1)*(1)=1 unit2
Find out the area of the function y=x^3 in the interval [-1,0]

the area of the shaded region in the interval [-1,0] is
A=1-(1/4)=3/4 unit2
step 2
Find out the area of the function y=-1 in the interval [0,1]
A=(1)*(1)=1 unit2
Find out the area of the function y=x^3 in the interval [0,1]

the area of the shaded region in the interval [0,1] is
A=1+1/4=5/4 unit2
the total area is
(3/4)+(5/4)=8/4=2 unit2