You can show it to Apple, but they may or may not provide a replacement. Typically, Apple branded accessories come with a One-Year Limited Warranty, which covers defects in materials and workmanship when used normally in accordance with Apple's published guidelines for a period of one year from the date of original retail purchase by the end-user purchaser.
The cable you have appears to have been beat up with use, so they may not cover it. Only Apple can tell you, which means you would need to take it to your closest Apple Store Genius Bar with a copy of your original purchase receipt and show it to them.
Cables aren't expensive items, so personally, I'd just buy a replacement cable and not go through the hassle of going to an Apple Store. In my opinion, Anker makes more durable cables for less money. You can check Amazon.com for options which meet your particular needs.