Question about Integration as the limit of a sum

Find the integral by the method of summation the values of :-
(a) integral of e^(-x) where the range of integration is from a to b.
(b) integral of e^(kx) where the range of integration is from a to b.

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This solution is comprised of a detailed explanation for finding the integral by the method of summation the values.
It contains step-by-step explanation for finding the integral by the method of summation the values of :-

(a) integral of e^(-x) where the range of integration is from a to b.
(b) integral of e^(kx) where the range of integration is from a to b.

Solution contains detailed step-by-step explanation.