I have tried to enhance the scripts previously given by Nora Diaz and Michel Marques. Thanks to them.

For a whole segment to uppercase/lowercase, you need to select all manually. So adding
Send, ˆa
as second line solves the problem :)

So, I propose this code for many ways of converting :

!x:: ; Alt X Convert word to capitalized or lowercase
Send {Right}
Send ^{Left}
Send +{Right}
Sleep 100
Send ^c
Sleep 200
Send +{F3}
Return

^l:: ; Ctrl L Convert segment to lowercase 1
Send, ^a
Send, ^c
Send, {Del}
Stringlower Clipboard, Clipboard
Send %Clipboard%
Return

!l:: ; Alt L Convert word to lowercase
Send, ^{Right}+^{Left}
Send, ^c
Send, {Del}
Stringlower Clipboard, Clipboard
Send %Clipboard%
Return

^u:: ; Ctrl u Convert segment to capitalized
Send, ^a
Send, ^c
Send, {Del}
StringUpper Clipboard, Clipboard
Send %Clipboard%
Return

!u:: ; Alt u Convert word to capitalized
Send, ^{Right}+^{Left}
Send, ^c
Send, {Del}
StringUpper Clipboard, Clipboard
Send %Clipboard%
Return