examine the area problem, and use sums of the form ∑_i f(x_i) δx_i as area under the curve y=f(x)
interpret the definite integral ∫ {from a to b} f(x)dx as area under the curve y=f(x) if f(x)>0
recognise the definite integral ∫ {from a to b} f(x)dx as a limit of sums of the form ∑_i f(x_i) δx_i
