I use Tick (https://www.tickspot.com/) for time tracking. There is no integration, but you can enter time manually or run timers. It's been wonderful for looking into how many hours were spent on similar jobs in the past for bidding purposes. Very easy to use interface.
Man, I'm just a Front End Dev, I get the designs and I code and I only landed this job 2 months ago :). Boss and admin team are taking care of it but I tell you what helps:
We use this app: https://www.tickspot.com along with Basecamp. Time tracking if done right helps them to assess what to quote, based on time tracking on previous projects. Nevertheless, company exists for over 10 years and it still seems like quoting time is the hardest part of dealing with clients as it's really hard to know what exactly it will take, especially with big projects. Sometimes clients suddenly remind themselves of a feature they wanted, mid-project, causing us having to redo a lot of what we have already coded.
As for freelance - quote twice more time than you think you'll need.
We use Tick at my company. Even though the website says it's free for 30 days, they have an option that is completely free but only allows one job to be open at a time. But you organize stuff by job, and the an put (I think) unlimited tasks under each job.
https://www.tickspot.com/time-tracking
There is a desktop app and a mobile app, with a stopwatch timer that you can use as well.
I looked around for something like this (iOS in my case) that supported multiple users, so I could capture my time, my wife could capture hers, etc, and we could see later on how much time we spent on different flipping tasks (sourcing, listing, photos, etc) as a whole. The only one I found that didn't require a paid account to do it was Tick, which I've been pretty happy with.
Check out our product, Tick.
It's simple web based time tracking that also has an iOS application and desktop timer. Check it out and let me know if you have any questions about our product.