# Math Help - Differentiation and Integral

1. ## Differentiation and Integral

It's similar to something I posted before but how would I show that
the integral from 0 to x of h(t)sin(x-t)dt exists?

I'm sure it's similar but the same with
the integral from 0 to x of h(t)cos(x-t)dt

2. Originally Posted by James234
It's similar to something I posted before but how would I show that
the integral from 0 to x of h(t)sin(x-t)dt exists?
What do you mean, "exists"?

Do you means the Riemann integral exists?
If that then yes it is true if $h(t)$ is continous.

Thus, since $\sin (x-t)$ is continous and $h(t)$ is continous thus is their product. And hence any continous function is Riemann integratable.