Find the area of the region bounded by y=x^4/3-4 , the x-axis,x=-1 , and x=1 ..
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area=int y dx over limits
area=int(1/3 x^4 -4) dx
area= 1/15 x^5 -4x over limits
area=1/15-4-(-1/15+4)=2/15-8 reduce that. Area negative means below the x axis.
area= 7 13/15= 7.866
And here is a neat numerical integration applet to demonstrate it.
enter xo=-1, x1=1, 10 steps, function 1/3*x^4 + 4