My book claims:
Fumaric acid can form intermolecular hydrogen bonds (strong) while maleic acid forms intramolecular hydrogen bonds (weak), hence fumaric acid has higher boiling point than maleic acid."
The intermolcular hydrogen bonds in fumaric acid are said to be stronger than the intramolecular hydrogen bonds in maleic acid, while I thought that intramolecular hydrogen bonds should be stronger than intermolecular hydrogen bonds. So, which one is correct?
Intramolecular hydrogen bonds do not have to be weak, but the strength of a hydrogen bond depends a lot on the $\ce{O-H\bond{....}O}$ angle. With intramolecular hydrogen bonds, it is often hard to achieve the perfect $180^\circ$ angle while the same is not a real exercise for intermolecular hydrogen bonds which have full degrees of freedom of movement on both sides.
In fact, I want to argue that maleic acid only forms intramolecular hydrogen bonds if there is no solvent (or crystal water) that can otherwise supply hydrogen bonds. If there is, all hydrogen-bonding sites — both donating and accepting — will be fully saturated with external hydrogen bonds instead; they are slightly stronger due to the better angle.
The question remains why fumaric acid — which is definitely unable to build up intramolecular hydrogen bonds — has a higher boiling point, because in theory maleic acid should also be able to form as many intermolecular hydrogen bonds. However, fumaric acid’s structure already dictates that it practically must form a network of coplanar molecules interacting with each other via hydrogen bond dimers from carboxylate to carboxylate. This is a very nice structure to keep. Maleic acid cannot form such an extensive network no matter how much it distorts. It will be restricted to much less favourable crystal structures meaning weaker intermolecular attraction.
In the liquid phase, fumaric acid will keep the near-sphere ordering somewhat intact, i.e. conserve a high number of hydrogen bonds to its neighbours. However maleic acid will probably stick with one fully intramolecular hydrogen bond that does not contribute to intermolecular attractions, thereby lowering its boiling point.
What your book (probably) meant is that the hydrogen bonds in fumaric acid, being intermolecular, does a better job of holding the molecules together, so it has a higher boiling point than maleic acid, which instead, displays intramolecular hydrogen bonding which doesn't hold the molecules together just as well.
