Proving Integrability of Constant Function f on [a,b]

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Suppose that f is integrable on [a,b]. Let c E \Re. Prove that cf is integrable on [a,b] and that
\int cf= c \int f
(both integrals goes from a to b i didn't kno how to put it in the integral)

I'm not sure how to go about this problem
Please help me out~
Thanks
 
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When you are completely "stuck", look back to the definitions.

How have you defined \int_a^b f(x) dx?
 
okay, i just got a hint saying that it would be best if we treat this separately with the cases c\leq0 and c\geq0.

how would that help me out? wouldn't it just be the same thing except it will be either negative or positive?
 
How have you defined \int_a^b f(x)dx?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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