EXAMPLE $5$ Evaluate the integral below.

$6$ex dx$4$

SOLUTION The function

f$($x$)=$ ex

is continuous everywhere and we know that an antiderivative is

F$($x$)=$ ex$,$

so Part $2$ of the Fundamental Theorem gives

$6$ex dx$4$

$=$ F$(6)$ F$(4)=$

Notice that the Fundamental Theorem of Calculus says we can use any antiderivative F of f$.$ So we may as well use the simplest one, namely

F$($x$)=$ ex$,$

instead of

ex $+7$

or

ex $+$ C$.$