Laplace Transform Question

Question

I was looking in my differential equations textbook and I found an interesting problem and I have no idea on how to approach it. I am supposed to let $F(s) = \mathcal{L} \{f(t) \} $ where $f(t)$ is piecewise continuous and of exponential order on $[0,\infty)$. Show that

$$\mathcal{L} \left\{ \int^{t}_{0} f(\tau)\space\text{d}\tau \right\} = \frac{1}{s} F(s)$$

is true.

Answer 1

HINT: Use the definition of the Laplace transform and integrate by parts.