Calculating the convolution of $\sin(t)/t$

Question

So how would I go about calculating the convolution of:

$$1* \sin(t)/t$$

This will be a simple looking integral, however $\sin$ or $\cos$ are not defined for infinity and negative infinity.

Answer 1

As stated, the convolution is simply the integral of the function, or

$$\int_{-\infty}^{\infty} dt \frac{\sin{t}}{t} = \pi$$