Relation between a and b when a random variable has exponential

Relation between a and b when a random variable has exponential pdf
f_x(x) = ae^{– b|x|}

Given F_x(x) = ae^{– b|x|}

F_x(x)=		^∞	F_x(x)dx
		_{– ∞}

1 =		^∞	ae^{– b\|x\|} .dx
		_{– ∞}

or 1 =		⁰	ae^{+ bx} dx +		^∞	ae^{– bx}.dx
		_{– ∞}			₀

or 1 =		ae^bx	+ bx		⁰	+		ae^{– bx}			^∞
		b			_{– ∞}			– b			₀

or 1 =	a	–	ae^{– b∞}	+		a		e^{– b∞} +	a	· 1
	b		b			– b			a

or 1 =	2a
	b

or 2a = b