I like doing this. Is it a known opening?

http://www.365chess.com/opening.php?m=2&n=15&ms=c4&ns=15

It's the English opening.

Hi lesmodolasontdescons--c4 is extremely common in the whole umbrella of Queen's Pawn openings, anything with 1. d4 and then a response by black to stop 2. e4, such as 1...d5, 1...Nf6, 1...f5, etc.  This is because white actually finds it very difficult to force e4 without a piece behind it; on the other hand if he starts the game with 1. e4 and later wants to push d4, this is usually possible since his queen on d1 provides defense.

So let's take the simple position after 1. d4 d5.  White knows it'll be a headache to force e4, so he plays 2. c4 instead.  This is a popular opening known as the Queen's Gambit and if black takes on c4, the pawn is easily recovered.  So black often declines it with 2...e6 and if white then plays 3. e3, we have the position from your diagram.  It's a little more accurate for white to play 3. Nc3 or 3. Nf3 first, then bring his c1 bishop out to f4 or g5.  By doing that prior to his e3 push, the bishop sees more excitement than it would otherwise.  That whole scheme of things though--settling for development with c4, e3, Nc3, Nf3, Bd3, 0-0, Qc2, etc. since e4 is so difficult--is certainly the right idea here.

Uhm, it's not an English Opening.  Based on the diagram, it's the position after 1.d4 d5 2.c4 e6 3.e3, which is a weak variation of the Queen's Gambit Declined.  If you are going to play d4 and c4, play 3.Nc3, not 3.e3.

e3 is typically played in what is called the Colle, which White then only plays c4 if either Black plays c6 prior (instead of c5) or if he goes into the Zukertort (1.d4 d5 2.Nf3 Nf6 3.e3 e6 4.Bd3 c5 5.b3 - Koltanowski is 5.c3).

Here, White is hemming in the Bishop while also trying to break up Black's center quickly.  The two ideas don't mix.

If you want to attack quickly, then 1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.Bg5 Be7 5.e3 with 6.Nf3 is stronger.