The number of miles you drive to work and back may or may not be taken into account by your car insurance company. Typically it is the amount of miles driven per year that will make a difference to your auto insurance provider. Insurance companies' rating system differ, as do state laws, so the number of miles driven may be used as a rating factor by your insurance company or more likely they offer a discount if you drive less than a certain number of miles annually.
The fewer miles you drive in a year the less risk you are to get in an accident though so rates are typically lower if you drive fewer miles. There is not an insurance industry standard for when all insurance providers give you a discount for driving few miles or that they raise your rates once you drive more than a certain amount of miles per year. It varies from one insurance company to another as does how much this rating factor affects your overall rates. Many insurance companies though instead offer discounts to motorists who drive a lower than average number of miles a year.
Your policy should say what you need to inform your insurance company of, such as changes with drivers, newly licensed household members, change of vehicles, and even perhaps the amount of miles driven. If your insurer requires that you tell them about changes in miles driven and you fail to inform them that you now are driving more miles to work and are in an accident typically it would still be covered but it really would ultimately be up to the terms of your policy and state laws. If you were in an accident on the way to work and it was covered but your insurer required you to tell them the distance you drive to work and back and you had failed to update them than your commute had increase then your insurer would of course now update your insurance policy and your premiums may then go up.
What you do not want to is misrepresent on purpose your mileage by telling your insurer you only drive 10 miles to work and back each day when you really go 50. If mileage is a rating factor and you give incorrect information such as this to your insurer than it could be considered misrepresentation, a form of fraud. To properly rate and insure you, your insurance company needs correct information on things such as the location of your car, drivers and the miles driven annual and some may even want to know how far you drive daily to work and back.
Auto insurance premiums in many instances are, in part, set by the information you provide about what purposes you drive for, how often you drive (i.e. to work or to school daily or if it is just a weekend car), and how far you drive per year. They may rate you on this information and can discount your policy even on it.
Some states use or are contemplating mileage based insurance but not all states may include this as a rating factor or an insurance company may or may not use the mileage put on a vehicle as part of their rating calculations.