Geodesic
Applying the Cauchy Integral
Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 689-693

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It could perhaps be reasonably maintained that for most students of calculus the definite integral is in fact the Cauchy Integral. That is to say, where F is a primitive of f.If done heuristically, the discussion of the Riemann integral serves two purposes. Firstly, it indicates that every continuous function has a primitive. 
Taylor, J. C. Applying the Cauchy Integral. Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 689-693. doi: 10.4153/CMB-1967-070-x
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     title = {Applying the {Cauchy} {Integral}},
     journal = {Canadian mathematical bulletin},
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     year = {1967},
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     number = {5},
     doi = {10.4153/CMB-1967-070-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-070-x/}
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