Just in case a picture helps...

The fundamental theorem of calculus tells us that if...

...we can form the integral function A using the limit definition, then...

... we can use an antiderivative to calculate the integral. And hence, because A(a) = 0...

As usual, straight continuous lines differentiate downwards. Hope this helps (with the general question - my broadband is too slow yet for me to see your jpg!), or doesn't further confuse.

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